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[[File:Black Hole Milkyway.jpg|200px|thumb|right|Simulated view of a black hole in front of the Milky Way. The hole has 10 solar masses and is viewed from a distance of {{Convert|600|km|0|abbr=on}}.<ref>{{cite web|url=http://www.spacetimetravel.org/expeditionsl/expeditionsl.html |last=Kraus |first=Ute |date=2005-03-20 |title=Step by Step into a Black Hole}}</ref>]] |
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{{General relativity|cTopic=Phenomena}} |
{{General relativity|cTopic=Phenomena}} |
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In [[general relativity]], a '''black hole''' is a region of space in which the [[gravitational field]] is so powerful that nothing, including [[electromagnetic radiation]] (e.g. [[visible light]]), can escape its pull after having fallen past its [[event horizon]]. The term derives from the fact that absorption of visible light renders the hole's interior invisible, and indistinguishable from the black [[outer space|space]] around it. |
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In [[astrophysics]], a '''black hole''' is a massive object whose [[gravitational field]] is so intense that it prevents any form of [[matter]] or [[radiation]] to escape. The term derives from the fact that absorption of visible light renders the hole's interior invisible, and indistinguishable from the black [[space]] around it. Black holes are predicted to exist through [[Solutions of the Einstein field equations|solutions]] of [[Einstein field equations|Einstein's field equations]] of [[general relativity]]. They are not directly observable, but several indirect observation techniques in different [[wavelengths]] have been developed and used to study the phenomena they induce in their environment. In particular, gasses caught by the gravitational field of a black hole are heated to considerably high [[temperatures]] before being swallowed and thereby emitting a significant amount of [[X-rays]]. So even if a black hole does not itself give off radiation, it may nevertheless be detectable by it's effect on it's surrounding environment. Such observations have resulted in the general scientific consensus that, barring a breakdown in our understanding of nature, black holes do exist in our [[universe]]. |
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Despite its invisible interior, a black hole may reveal its presence through interaction with matter orbiting the event horizon. For example, a black hole may be perceived by tracking the movement of a group of stars that orbit its center. Alternatively, one may observe gas (from a nearby star, for instance) that has been drawn into the black hole. The gas spirals inward, heating up to very high temperatures and emitting large amounts of [[radiation]] that can be detected from earthbound and earth-orbiting telescopes.<ref>{{cite web |url=http://imagine.gsfc.nasa.gov/docs/science/know_l1/compact_binary.html |title=Gamma-rays from Black Holes and Neutron Stars |publisher=[[Goddard Space Flight Center]]}}</ref><ref>{{cite journal |arxiv=astro-ph/0606352 |doi=10.1146/annurev.astro.44.051905.092532 |title=X-Ray Properties of Black-Hole Binaries |year=2006 |author=Ronald A. Remillard; Jeffrey E. Mc Clintock |journal=Annual Review of Astronomy and Astrophysics |volume=44 |pages=49–92|s2cid=119417042 }}</ref> Such observations have resulted in the general scientific consensus that—barring a breakdown in our understanding of nature—black holes do exist in our [[universe]].<ref name="CMS1999">{{cite journal |doi=10.1088/0264-9381/16/12A/301 |arxiv=astro-ph/9912186 |year=1999 |date=December 1999 |title=Astrophysical evidence for the existence of black holes |journal=[[Classical and Quantum Gravity]] |volume=16 |issue=12A |pages=A3–A21|last1=Celotti |first1=A. |last2=Miller |first2=J. C. |last3=Sciama |first3=D. W. |s2cid=17677758 }}</ref> |
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==Introduction and Terminology== |
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A black hole is often defined by the [[escape velocity]] that would have to be attained to escape from the gravitational pull exerted upon an object. For example, the escape velocity of an object on [[earth]] is equal to 11 km/s. No matter the object, a rocket or baseball, it must go at least 11 km/s. The escape velocity of an object depends on how [[compact]] it is; that is, the [[ratio]] of its [[mass]] to [[radius]]. A black hole is an object so compact that, within a certain distance of it, even the [[speed of light]] is not fast enough to escape. |
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The idea of an object with [[gravity]] strong enough to prevent light from escaping was proposed in 1783 by [[John Michell]],<ref name="Michell1784">{{cite journal |last=Michell |first=J. |year=1784 |journal=[[Philosophical Transactions of the Royal Society]] |volume=74 |pages=35–57 |doi=10.1098/rstl.1784.0008 |bibcode=1784RSPT...74...35M|jstor=106576 |title=On the Means of Discovering the Distance, Magnitude, &c. of the Fixed Stars, in Consequence of the Diminution of the Velocity of Their Light, in Case Such a Diminution Should be Found to Take Place in any of Them, and Such Other Data Should be Procured from Observations, as Would be Farther Necessary for That Purpose. By the Rev. John Michell, B. D. F. R. S. In a Letter to Henry Cavendish, Esq. F. R. S. and A. S.|url=https://zenodo.org/record/1432270 }}</ref> an amateur British astronomer. In 1795, [[Pierre-Simon Laplace]], a French physicist independently came to the same conclusion.<ref>{{cite web |url=http://library.thinkquest.org/25715/discovery/conceiving.htm#darkstars |title=Dark Stars (1783) |accessdate=2008-05-28 |quote= |publisher=[[Thinkquest]] }}</ref><ref>{{cite book |first=Werner |last=Israel |authorlink=Werner Israel |chapter=The Chandrasekhar limit (1929–35) |chapter-url=https://books.google.com/books?id=Vq787qC5PWQC&pg=PA212 |editor=[[Stephen Hawking]] and [[Werner Israel]] |title=Three hundred years of gravitation |publisher=[[Cambridge University Press]] |location=[[Cambridge]] |year=1989 |pages=212–216 |isbn=0-521-37976-8}}</ref> However, such "Newtonian black holes" are very different from black holes in general relativity. They prevent only light from escaping (not, for example, a rocket ship) and only in certain Newtonian models of light (such as an [[emission theory]]). |
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A black hole's mass is concentrated at a point called a [[singularity]]. Surrounding the singularity is a theoretical [[sphere]] called the [[event horizon]]. The event horizon marks the '[[point of no return]]', a boundary that, if crossed, inevitably leads falling matter and radiation towards the singularity. This sphere is a kind of spatial extension of the black hole. For a black hole of mass equal to that of the [[Sun]], its radius is about 3 km. At a distance of about 10<sup>6</sup> km, a black hole has no more attraction than any other body of the same mass. For example, if the sun was replaced by a black hole of the same mass, the orbits of its [[planets]] would remain unchanged. |
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Black holes, as currently understood, are described by the general theory of relativity. This theory predicts that when a large enough amount of [[mass]] is present in a [[hoop conjecture|sufficiently small region of space]], all [[world line|paths through space]] are warped inwards towards the center of the [[volume]], preventing all matter and radiation within it from escaping. |
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There are several types of black holes. When they form as a result of the [[gravitational collapse]] of a [[star]], they are called [[stellar black hole|stellar black holes]]. Black holes found at the center of galaxies have a mass up to several billion [[solar masses]] and are called [[supermassive black hole|supermassive black holes]] simply because of their size. Between these two scales, it is believed that there are ''intermediate black holes'' with a mass of several thousand solar masses. Black holes with very small masses, believed to have formed early in the history of the [[Universe]], during the [[Big Bang]], are also considered, and are referred to as [[primordial black holes]]. Their existence is, at present, not confirmed. |
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While general relativity describes a black hole as a region of empty space with a point-like [[gravitational singularity|singularity]] at the center and an event horizon at the outer edge, the description changes when the effects of [[quantum mechanics]] are taken into account. Research indicates that, rather than holding captured matter forever, black holes slowly leak a form of thermal energy called [[Hawking radiation]] and have a finite lifetime.<ref name="Nature248 ">{{cite journal |journal=Nature |volume=248 |year=1974 |pages=30–31 |title=Black Hole Explosions |last=Hawking |first=Stephen |issue=5443 |doi=10.1038/248030a0|s2cid=4290107 }}</ref><ref name="McDonald">{{cite web |last=McDonald |first=Kirk T. |title = Hawking-Unruh Radiation and Radiation of a Uniformly Accelerated Charge |date=1998-02-03 |url=http://www.hep.princeton.edu/~mcdonald/accel/unruhrad.pdf |publisher=[[Princeton University]]}}</ref><ref>{{cite book |first=Stephen W. |last=Hawking |authorlink=Stephen Hawking |coauthors=[[Roger Penrose]] |title=The Nature of Space and Time |publisher=[[Princeton University Press]] |location=[[Princeton, New Jersey]] |year=2000 |page=[http://books.google.com/books?id=LstaQTXP65cC&pg=PA44 44] |isbn=0-691-05084-8 |oclc=45785998}}</ref> The as yet unknown theory of [[quantum gravity]] is believed to give the fully correct description of black holes. |
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It is impossible to directly observe a black hole. However, it is possible to infer its presence by its gravitational action on the surrounding [[environment]], particularly with [[microquasars]] and [[Active galactic nucleus|active galactic nuclei]], where material falling into a nearby black hole is significantly heated and emits a large amount of X-ray radiation. This observation method allows [[astronomers]] to detect their existence. The only objects that agree with these observations and are consistent within the framework of [[general relativity]] are black holes. |
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== |
==Etymology== |
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The term ''black hole'' to describe this phenomenon dates from the mid-1960s, though its precise origins are unclear. Physicist [[John Archibald Wheeler|John Wheeler]] is widely credited with coining it in his 1967 public lecture ''Our Universe: the Known and Unknown'', as an alternative to the more cumbersome "gravitationally completely collapsed star". However, Wheeler insisted that someone else at the conference had coined the term and he had merely adopted it as useful shorthand. The term was also cited in a 1964 letter by Anne Ewing to the [[American Association for the Advancement of Science|AAAS]]:<ref>{{cite web |title=Black Hole |work=World Wide Words |first=Michael |last=Quinion |authorlink=Michael Quinion |url=http://www.worldwidewords.org/topicalwords/tw-bla1.htm |accessdate=2008-06-17}}</ref> |
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[[Image:Black_hole_lensing_web.gif|thumb|right|240px|Schwarzchild black hole|Simulation of [[Gravitational lensing]] by a black hole which distorts a [[galaxy]] in the background.]] |
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{{cquote|''According to Einstein’s general theory of relativity, as mass is added to a degenerate star a sudden collapse will take place and the intense gravitational field of the star will close in on itself. Such a star then forms a "black hole" in the universe.''}} |
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The idea of a body so massive that even light could not escape was put forward by [[geologist]] John Michell in a letter written to [[Henry Cavendish]] in 1783 to the [[Royal Society]]: |
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The phrase had already entered the language years earlier as the [[Black Hole of Calcutta]] incident of 1756 in which 146 Europeans were locked up overnight in punishment cell of barracks at [[Fort William, India|Fort William]] by [[Siraj ud-Daulah]], and all but 23 perished.<ref>{{cite web |url=http://www.etymonline.com/index.php?term=black+hole |title=black hole |work=Online Etymology Dictionary |date=November 2001 |year=2001 |first=Douglas |last=Harper |authorlink=Douglas Harper}}</ref> |
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{{quote|If the semi-diameter of a sphere of the same density as the Sun were to exceed that of the Sun in the proportion of 500 to 1, a body falling from an infinite height towards it would have acquired at its surface greater velocity than that of light, and consequently supposing light to be attracted by the same force in proportion to its vis inertiae, with other bodies, all light emitted from such a body would be made to return towards it by its own proper gravity.|[[John Michell]]<ref name="Michell1784">{{citation |last=Michell |first=J. |year=1784 |title=On the Means of Discovering the Distance, Magnitude, &c. of the Fixed Stars, in Consequence of the Diminution of the Velocity of Their Light, in Case Such a Diminution Should be Found to Take Place in any of Them, and Such Other Data Should be Procured from Observations, as Would be Farther Necessary for That Purpose |journal=Phil. Trans. R. Soc. (London) |volume=74 |pages=35–57|url=http://www.jstor.org/pss/106576}}.</ref>}} |
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The phenomenon appeared in science fiction in a radio episode of ''[[Space Patrol (1950s)|Space Patrol]]'' which aired October 25, 1952, in which it was called a "cycloplex" or a "hole in space".{{Citation needed|date=March 2009}} |
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In 1796, mathematician [[Pierre-Simon Laplace]] promoted the same idea in the first and second editions of his book ''Exposition du système du Monde'' (it was removed from later editions).<ref>{{cite web |url=http://library.thinkquest.org/25715/discovery/conceiving.htm#darkstars |title=Dark Stars (1783) |accessdate=2008-05-28 |quote= |publisher=[[Thinkquest]] }}</ref><ref>Laplace; see Israel, Werner (1987), "Dark stars: the evolution of an idea", in Hawking, Stephen W. & Israel, Werner, 300 Years of Gravitation, Cambridge University Press, Sec. 7.4</ref> Such "[[dark star]]s" were largely ignored in the nineteenth century, since light was then thought to be a massless wave and therefore not influenced by gravity. Unlike the modern black hole concept, the object behind the horizon is assumed to be stable against collapse. |
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==What makes it impossible to escape from black holes?== |
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In 1915, [[Albert Einstein]] developed his general theory of relativity, having earlier shown that gravity does in fact influence light's motion. A few months later, [[Karl Schwarzschild]] gave the [[Schwarzschild metric|solution]] for the gravitational field of a point mass and a spherical mass,<ref name ="Schwarzschild1916"/> showing that a black hole could theoretically exist. The [[Schwarzschild radius]] is now known to be the radius of the [[event horizon]] of a non-rotating black hole, but this was not well understood at that time, for example Schwarzschild himself thought it was not physical. Johannes Droste, a student of [[Hendrik Lorentz]], independently gave the same solution for the point mass a few months after Schwarzschild and wrote more extensively about its properties. |
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{| align="right" class="wikitable" style="margin:1ex 1ex 1ex 1ex" width="400" |
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|-width |
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|[[File:BH-no-escape-1.svg]]<br/>Far away from the black hole a particle can move in any direction. It is only restricted by the speed of light. |
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|[[File:BH-no-escape-2.svg]]<br/>Closer to the black hole spacetime starts to deform. There are more paths going towards the black hole than paths moving away. |
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|[[File:BH-no-escape-3.svg]]<br/>Inside of the event horizon all paths bring the particle closer to the center of the black hole. It is no longer possible for the particle to escape. The diagrams here are effectively Finkelstein diagrams using an advanced time parameter.<ref>{{cite book |first=Stephen W. |last=Hawking |coauthors=[[George Ellis]] |title=The large scale structure of space-time |publisher=[[Cambridge University Press]] |location=[[Cambridge]] |year=1973 |page=[http://books.google.com/books?id=QagG_KI7Ll8C&pg=PA152 152] |isbn=0-521-09906-4 |oclc=16002677}}</ref> |
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|} |
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Popular accounts commonly try to explain the black hole phenomenon by using the concept of [[escape velocity]],<ref>{{cite web |url=http://amazing-space.stsci.edu/resources/explorations/blackholes/teacher/sciencebackground.html |title=No Escape: The Truth About Black Holes |publisher=[[Space Telescope Science Institute]] |accessdate=2009-03-14}}</ref><ref>{{cite web |last=Kirkham |first=Jesse |url=http://www.jessekirkham.com/blackholes.htm |title=Black Holes - Relativistic escape velocity |accessdate=2009-03-03}}{{Unreliable source?|date=March 2009}}</ref> the speed needed for a vessel starting at the surface of a massive object to completely clear the object's gravitational field. It follows from [[Newton's law of universal gravitation|Newton's law of gravity]] that a sufficiently dense object's escape velocity will equal or even exceed the [[speed of light]]. Citing that nothing can exceed the speed of light they then infer that nothing would be able to escape such a dense object.<ref>{{cite web |first=Ralph |last=Bassett |coauthors=Karyn Blaser, Anna Kaltenboeck, Jay Meattle, Anna Lindgren-Streicher and Ryan Vinelli |url=http://hepguru.com/blackholes/characteristics.htm |title=Characteristics of Black Holes |year=2002 |date=Spring 2002}}</ref> However, the argument can only be seen as an incomplete analogy. It explains neither why light should be affected by gravity in the first place, why it cannot travel beyond the horizon, nor why a rocket-powered spaceship would not be able to break free. |
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Two concepts introduced by Albert Einstein are needed to explain the phenomenon. The first is that time and space are not two independent concepts, but are interrelated forming a single continuum, [[spacetime]]. This continuum has some special properties. An object is not free to move around spacetime at will; it must always move forward in time and cannot change its position in space faster than the speed of light.<ref>{{cite web |last=Schwarz |first=Patricia |publisher=Caltech |url=http://www.theory.caltech.edu/people/patricia/sptmtop.html |title=What is "spacetime"? |accessdate=2009-03-03}}</ref> This is the main result of the theory of [[special relativity]]. |
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In 1930, [[astrophysicist]] [[Subrahmanyan Chandrasekhar]] calculated using general relativity that a non-rotating body above 1.44 solar masses (the [[Chandrasekhar limit]]) would collapse. His arguments were opposed by [[Arthur Eddington]], who believed that something would inevitably stop the collapse. Eddington was partly correct: a [[white dwarf]] slightly more massive than the Chandrasekhar limit will collapse into a [[neutron star]]. But in 1939, [[Robert Oppenheimer]] and others predicted that stars above approximately three solar masses (the [[Tolman-Oppenheimer-Volkoff limit]]) would collapse into black holes for the reasons presented by Chandrasekhar.<ref>[http://prola.aps.org/abstract/PR/v55/i4/p374_1 On Massive Neutron Cores], J. R. Oppenheimer and G. M. Volkoff, ''Physical Review'' '''55''', #374 (15 February 1939), pp. 374–381.</ref> |
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The second concept is the base of general relativity; mass deforms the structure of this spacetime.<ref>{{cite news |first=Anushka |last=Asthana |coauthors=David Smith |url=http://www.guardian.co.uk/science/2007/apr/15/spaceexploration.universe |title=Einstein was right: space and time bend |work=[[The Guardian]] |date=2007-04-25 |accessdate=2009-03-14}}</ref> The effect of a mass on spacetime can informally be described as tilting the direction of time towards the mass. As a result, objects tend to move towards masses. This is experienced as gravity. This tilting effect becomes more pronounced as the distance to the mass becomes smaller.<ref>{{cite web |url=http://www.scienceblog.com/cms/node/6815 |title=Quantum Theory, Gravitoelectric Fields, Space-Time, etc... |date=2005-01-28 |accessdate=2009-03-14}}{{Unreliable source?|date=March 2009}}</ref> At some point close to the mass, the tilting becomes so strong that all the possible paths an object can take lead towards the mass.<ref>{{cite arXiv |eprint=gr-qc/9707012 |last1=Townsend | first1=P. K. |title=Black Holes |class=gr-qc |year=1997}}</ref> This implies that any object that crosses this point can no longer get further away from the mass, not even using powered flight. This point is called the [[event horizon]]. |
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Oppenheimer and his co-authors used [[Schwarzschild metric|Schwarzschild's system of coordinates]] (the only coordinates available in 1939), which produced [[mathematical singularity|mathematical singularities]] at the [[Schwarzschild radius]], in other words the equations broke down at the Schwarzschild radius because some of the terms were [[infinity|infinite]]. This was interpreted as indicating that the Schwarzschild radius was the boundary of a "bubble" in which time "stopped". The collapsed stars were briefly known as "frozen stars",{{fact}} as the calculations indicated that an outside observer would see the surface of the star frozen in time at the instant where its collapse takes it inside the Schwarzschild radius. But many physicists could not accept the idea of time standing still inside the Schwarzschild radius, and there was little interest in the subject for over 20 years. |
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In 1958, [[David Finkelstein]] broke the deadlock over "stopped time" and introduced the concept of the [[event horizon]] by presenting [[Eddington-Finkelstein coordinates]], which enabled him to show that "The Schwarzschild surface r = 2 m is not a singularity but acts as a perfect unidirectional membrane: causal influences can cross it in only one direction".<ref>D. Finkelstein (1958). "Past-Future Asymmetry of the Gravitational Field of a Point Particle". Phys. Rev. 110: 965–967. </ref> All theories up to this point, including Finkelstein's, covered only non-rotating, uncharged black holes. |
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In 1967, astronomers discovered [[pulsars]],<ref>{{cite journal |
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| last=Hewish | first=Antony | coauthors=S J Bell, J D H Pilkington, P F Scott, R A Collins |
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| title=Observation of a Rapidly Pulsating Radio Source |
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| journal=Nature | year=1968 |
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| volume=217 | issue= | pages=709–713 |
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| url=http://www.nature.com/nature/journal/v235/n5332/abs/235037a0.html |
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| accessdate=2007-07-06 | doi=10.1038/217709a0 }}</ref> <ref>{{cite journal |
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| last=Pilkington | first=J D H | coauthors=A Hewish, S J Bell, T W Cole |
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| title=Observations of some further Pulsed Radio Sources |
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| journal=Nature | year=1968 |
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| volume=218 | issue= | pages=126–129 |
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| url=http://www.nature.com/nature/journal/v218/n5137/pdf/218126a0.pdf |
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| accessdate=2007-07-06 | doi=10.1038/218126a0 }}</ref> and within a few years could show that the known pulsars were rapidly rotating [[neutron star]]s. Until that time, neutron stars were also regarded as just theoretical curiosities. So the discovery of pulsars awakened interest in all types of ultra-dense objects that might be formed by gravitational collapse. |
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==Properties: mass, charge, and angular momentum== |
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Physicist [[John Archibald Wheeler|John Wheeler]] is widely credited with coining the term ''black hole'' in his 1967 public lecture ''Our Universe: the Known and Unknown'', as an alternative to the more cumbersome "gravitationally completely collapsed star". However, Wheeler insisted that someone else at the conference had coined the term and he had merely adopted it as useful shorthand. The term was also cited in a 1964 letter by Anne Ewing to the [[AAAS]]: |
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The [[No hair theorem]] states that in a steady state, a black hole has only three independent physical properties: [[mass]], [[electric charge|charge]] and [[angular momentum]].<ref>{{cite journal |last=Heusler |first=Markus |year=1998 |title=Stationary Black Holes: Uniqueness and Beyond |journal=Living Rev. Relativity |volume=1 |number=6 |page=6 |doi=10.12942/lrr-1998-6 |doi-access=free |pmid=28937184 |pmc=5567259 |url=http://www.livingreviews.org/Articles/Volume1/1998-6heusler/ |bibcode=1998LRR.....1....6H}}</ref> Any two black holes that share the same values for these properties are indistinguishable. When a black hole swallows matter, its horizon oscillates like a membrane with internal friction, a [[dissipative system]]. This contrasts with other fundamental physical objects, which behave in a way that is time reversible. |
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{{quote|According to Einstein’s general theory of relativity, as mass is added to a degenerate star a sudden collapse will take place and the intense gravitational field of the star will close in on itself. Such a star then forms a "black hole" in the universe.|Ann Ewing|letter to ''AAAS''<ref>{{cite web|title=Black Hole|work=World Wide Words|author=Michael Quinion|url=http://www.worldwidewords.org/topicalwords/tw-bla1.htm|accessdate=2008-06-17}}</ref>}} |
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Because a black hole only has a few parameters, a great deal of information is lost when a star collapses to form a black hole. The black hole irreversibly settles down to a simple final state. In classical theories described by a Hamiltonian, [[Liouville's theorem]] guarantees that information is always preserved, so that the initial state can be reconstructed from the final state, in principle. Liouville's theorem fails for dissipative systems, like a viscous fluid. In that case the fluid eventually stops, irreversibly hiding information about the initial conditions. In a fluid, the lost information is presumably encoded in a complicated way in the motion of the atoms. For a black hole, it is hard to see where the information is hiding. |
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==Properties and Features== |
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{{main|Properties and features of black holes}} |
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===The No-hair theorem=== |
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The loss of information in black holes is puzzling, because General Relativity is a Lagrangian theory, which superficially appears to be time reversible and Hamiltonian. But because of the horizon, a black hole is not time reversible{{spaced ndash}}it swallows matter but it never spits it out. This irreversible character is an even more serious problem in quantum mechanics, because a quantum theory can only be properly formulated when a system is non-dissipative. Physicists call the conflict between quantum mechanics and black hole dynamics the [[black hole information paradox]]. |
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According to the [[No hair theorem|"No Hair" theorem]] a black hole has only three independent physical properties: [[mass]], [[electric charge|charge]] and [[angular momentum]].<ref>{{citation|last=Heusler |first=M. |year=1998 |title=Stationary Black Holes: Uniqueness and Beyond |journal=Living Rev. Relativity |volume=1 |number=6 |url=http://www.livingreviews.org/Articles/Volume1/1998-6heusler/}}</ref> Any two black holes that share the same values for these properties are indistinguishable. This contrasts with other astrophysical objects such as stars, which have very many—possibly infinitely many—parameters. Consequently, a great deal of information is lost when a star collapses to form a black hole. As [[Physical information|information]] is preserved in most physical theories, the loss of information in black holes is puzzling. Physicists refer to this as the [[black hole information paradox]]. |
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The No Hair theorem makes assumptions about the nature of our universe and the matter |
The No Hair theorem makes some assumptions about the nature of our universe and the matter it contains, and other assumptions lead to different conclusions. For example, if nature allows [[magnetic monopole]]s, which is theoretically possible but they have never been observed, then black holes could also have [[magnetic charge]]. If there are long range gauge forces other than electromagnetism, then black holes could be charged under those fields as well. |
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A charged black hole repels other like charges just like any other charged object, despite the fact that photons, the particles responsible for electric and magnetic forces, can't escape. The reason is that electric charge is always visible far away, by [[Gauss's law]], so that no matter what happens inside a big sphere, so long as no charged particles go in or out, the total electric flux stays the same. When charge falls into a black hole, electric field lines remain, and these field lines remember the total charge of all the infalling matter. The electric field lines eventually spread out evenly over the surface of the black hole, settling down to a uniform field-line density on the surface. The black hole acts in this regard like a classical conducting sphere with a definite resistivity.<ref>{{cite book |first=Kip S. |last=Thorne |authorlink=Kip Thorne |coauthors=[[Richard H. Price]] and Douglas A. MacDonald |title=Black holes: the membrane paradigm |publisher=[[Yale University Press]] |location=[[New Haven, Connecticut]] |year=1986 |pages= |isbn=0-300-03770-8}}{{page needed|date=April 2013}}</ref> |
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===Classification=== |
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Black holes in more than four dimensions, or in [[Anti de Sitter space]], can have all sorts of "hair". This is important for extensions of General Relativity like [[string theory]] or [[Kaluza Klein theory]], but in our apparently four-dimensional, very nearly flat universe, the no-hair theorem should hold.<ref>{{cite journal |arxiv=id=0803.0732|doi=10.1088/0067-0049/180/2/225 |title=Five-Year ''Wilkinson Microwave Anisotropy Probe'' Observations: Data Processing, Sky Maps, and Basic Results |year=2009 |author=Hinshaw, G. |journal=The Astrophysical Journal Supplement Series |volume=180 |issue=2 |pages=225–245|s2cid=3629998 }}</ref> |
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====By physical properties==== |
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===Black hole types=== |
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The simplest black hole is one that has mass but neither charge nor angular momentum. These black holes are often referred to as [[Schwarzschild metric|Schwarzschild black hole]]s after the physicist [[Karl Schwarzschild]] who discovered this [[Solutions of the Einstein field equations|solution]] in 1915.<ref name="Schwarzschild1916">{{Citation |
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The simplest black hole is one that has mass but neither charge nor angular momentum. These black holes are often referred to as [[Schwarzschild metric|Schwarzschild black hole]]s after the physicist [[Karl Schwarzschild]] who discovered this [[Solutions of the Einstein field equations|solution]] in 1915.<ref name="Schwarzschild1916">{{cite journal |
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}}.</ref> It was the first non-trivial [[Exact solutions in general relativity|exact solution]] to the [[Einstein equations]] to be discovered, and according to [[Birkhoff's theorem (relativity)|Birkhoff's theorem]], the only [[Vacuum solution (general relativity)|vacuum solution]] that is [[Spherically symmetric spacetime|spherically symmetric]]. For real world physics this means that there is no observable difference between the gravitational field of such a black hole and that of any other spherical object of the same mass—for example a spherical star or planet—once one is in the empty space outside the object. The popular notion of a black hole "sucking in everything" in its surroundings is therefore incorrect; the external gravitational field, far from the event horizon, is essentially like that of ordinary massive bodies. |
}}.</ref> It was the first non-trivial [[Exact solutions in general relativity|exact solution]] to the [[Einstein equations]] to be discovered, and according to [[Birkhoff's theorem (relativity)|Birkhoff's theorem]], the only [[Vacuum solution (general relativity)|vacuum solution]] that is [[Spherically symmetric spacetime|spherically symmetric]]. For real world physics this means that there is no observable difference between the gravitational field of such a black hole and that of any other spherical object of the same mass—for example a spherical star or planet—once one is in the empty space outside the object. The popular notion of a black hole "sucking in everything" in its surroundings is therefore incorrect; the external gravitational field, far from the event horizon, is essentially like that of ordinary massive bodies. |
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More general black hole solutions were discovered later in the 20th century. The [[Reissner-Nordström metric|Reissner-Nordström solution]] describes a black hole with electric charge, while the [[Kerr metric|Kerr solution]] yields a rotating black hole. The most general known [[Stationary spacetime|stationary]] black hole solution is the [[Kerr-Newman metric]], having both charge and angular momentum. All these general solutions share the property that they converge to the Schwarzschild solution at distances that are large compared to the ratio of charge and angular momentum to mass (in [[natural units]]). |
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Electrically charged non-rotating black holes are described by the [[Reissner-Nordström metric|Reissner-Nordström solution]], developed by [[Hans Reissner]]<ref>{{cite journal | last = Reissner | first = H | year = 1916 | title = Über die Eigengravitation des elektrischen Feldes nach der Einstein'schen Theorie | journal = Annalen der Physik | volume = 50 | pages = 106–120 | doi = 10.1002/andp.19163550905}}</ref> and [[Gunnar Nordström]].<ref>{{cite journal | last = Nordström | first = G | authorlink = Gunnar Nordström | year = 1918 | title = On the Energy of the Gravitational Field in Einstein's Theory | journal = Verhandl. Koninkl. Ned. Akad. Wetenschap., Afdel. Natuurk., Amsterdam | volume = 26 | pages = 1201–1208}}</ref> |
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While the mass of a black hole can take any (positive) value, the other two properties, charge and angular momentum, are constrained by the mass. In natural units, the total charge ''Q'' and the total angular momentum ''J'' are expected to satisfy ''Q''<sup>2</sup>+(''J''/''M'')<sup>2</sup> ≤ ''M''<sup>2</sup> for a black hole of mass ''M''. Black holes saturating this inequality are called [[extremal black hole|extremal]]. Solutions of Einstein's equations violating the inequality do exist, but do not have a horizon. These solutions have [[Naked singularity|naked singularities]] and are deemed ''unphysical'', as the [[cosmic censorship hypothesis]] states that it is impossible for such singularities to form due to the generic gravitational collapse of [[Energy conditions|realistic matter]].<ref>{{cite arXiv |eprint=gr-qc/9710068 |last1=Wald | first1=Robert M. |title=Gravitational Collapse and Cosmic Censorship |class=gr-qc |year=1997}}</ref> This is supported by numerical simulations.<ref>For a discussion of these numerical simulations see {{cite journal |last=Berger |first=Beverly K. |year=2002 |title=Numerical Approaches to Spacetime Singularities |journal=Living Reviews in Relativity |volume=5 |issue=1 |page=1 |doi=10.12942/lrr-2002-1 |doi-access=free |pmid=28179859 |pmc=5256073 |arxiv=gr-qc/0201056}}</ref> |
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Mathematician [[Roy Kerr]] presented the [[Kerr metric|Kerr solution]] in 1963, showing how this could be used to describe a [[rotating black hole]].<ref>{{cite web|url=http://prola.aps.org/abstract/PRL/v11/i5/p237_1|title=R. P. Kerr, "Gravitational field of a spinning mass as an example of algebraically special metrics", ''Phys. Rev. Lett.'' '''11''', 237 (1963)}}</ref> In addition to its theoretical interest, Kerr's work made black holes more believable for astronomers, since black holes are formed from stars and all known stars rotate. |
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Black holes forming from the collapse of stars are expected—due to the relatively large strength of [[electromagnetism|electromagnetic force]]—to retain the nearly neutral charge of the star. Rotation, however, is expected to be a common feature of compact objects, and the black-hole candidate binary X-ray source [[GRS 1915+105]]<ref>{{cite journal |doi=10.1086/508457 |url=http://www.iop.org/EJ/article/0004-637X/652/1/518/65488.web.pdf |arxiv=astro-ph/0606076 |title=The Spin of the Near-Extreme Kerr Black Hole GRS 1915+105 |year=2006 |author=Mcclintock, Jeffrey E. |journal=The Astrophysical Journal |volume=652 |pages=518–539|s2cid=1762307 }}</ref> appears to have an angular momentum near the maximum allowed value. |
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The most general known [[Stationary spacetime|stationary]] black hole solution is the [[Kerr-Newman metric]], discovered by physicist [[Ezra T. Newman|Ezra Newman]] et al<ref>Newman, Ezra and Janis, Allen. "Note on the Kerr Spinning-Particle Metric," ''Journal of Mathematical Physics'', volume 6, pages 915-917 (1965).</ref><ref>Newman, Ezra et al. "Metric of a Rotating, Charged Mass," ''Journal of Mathematical Physics'', volume 6, pages 918-919 (1965).</ref> having both charge and angular momentum. All these general solutions share the property that they converge to the Schwarzschild solution at distances that are large compared to the ratio of charge and angular momentum to mass (in [[natural units]]). |
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While the mass of a black hole can take any positive value, the charge and angular momentum are constrained by the mass. In natural units , the total charge ''Q'' and the total angular momentum ''J'' are expected to satisfy ''Q''<sup>2</sup>+(''J''/''M'')<sup>2</sup> ≤ ''M''<sup>2</sup> for a black hole of mass ''M''. Black holes saturating this inequality are called [[extremal black hole|extremal]]. Solutions of Einstein's equations violating the inequality do exist, but do not have a horizon. These solutions have [[Naked singularity|naked singularities]] and are deemed ''unphysical'', as the [[cosmic censorship hypothesis]] rules out such singularities due to the generic gravitational collapse of [[Energy conditions|realistic matter]].<ref>For a review see {{citation |last=Wald |first=Robert. M. |author-link=Robert Wald |title=Gravitational Collapse and Cosmic Censorship |year=1997 |url=http://arxiv.org/abs/gr-qc/9710068}}.</ref> This is supported by numerical simulations.<ref>For a discussion of these numerical simulations see {{Citation| last=Berger | first=Beverly K. | year=2002 | url=http://www.livingreviews.org/lrr-2002-1 | title=Numerical Approaches to Spacetime Singularities | journal=Living Rev. Relativity | volume=5 |access-date=2007-08-04}}.</ref> |
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Due to the relatively large strength of the [[electromagnetism|electromagnetic force]], black holes forming from the collapse of stars are expected to retain the nearly neutral charge of the star. Rotation, however, is expected to be a common feature of compact objects, and the black-hole candidate binary X-ray source [[GRS 1915+105]]<ref>{{citation |first1=Jeffrey E. |last1=McClintock |first2=Rebecca |last2=Shafee |first3=Ramesh |last3=Narayan |first4=Ronald A. |last4=Remillard |first5=Shane W. |last5=Davis |first6=Li-Xin |last6=Li |title=The Spin of the Near-Extreme Kerr Black Hole GRS 1915+105 |journal=Astrophys.J. |volume=652 |year=2006 |pages=518–539 |url=http://arxiv.org/abs/astro-ph/0606076}}.</ref> appears to have an angular momentum near the maximum allowed value. |
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====By mass==== |
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===Sizes=== |
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{|align="right" class="wikitable" style="margin: 1ex" |
{|align="right" class="wikitable" style="margin: 1ex" |
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! Class !! Mass !! Size |
! Class !! Mass !! Size |
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|[[Supermassive black hole]] ||style="text-align: center;"| ~10<sup>5</sup> - 10<sup>9</sup> M<sub>[[Sun]]</sub> ||style="text-align: center;"| ~0. |
|[[Supermassive black hole]] ||style="text-align: center;"| ~10<sup>5</sup> - 10<sup>9</sup> M<sub>[[Sun]]</sub> ||style="text-align: center;"| ~0.001–10 [[Astronomical unit|AU]] |
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|- |
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|[[Intermediate-mass black hole]] ||style="text-align: center;"| ~10<sup>3</sup> M<sub>[[Sun]]</sub> ||style="text-align: center;"| ~10<sup>3</sup> km = R<sub>[[Earth]]</sub> |
|[[Intermediate-mass black hole]] ||style="text-align: center;"| ~10<sup>3</sup> ''M''<sub>[[Sun]]</sub> ||style="text-align: center;"| ~10<sup>3</sup> km = ''R''<sub>[[Earth]]</sub> |
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|- |
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|[[Stellar black hole|Stellar-mass]] ||style="text-align: center;"| ~10 M<sub>[[Sun]]</sub> ||style="text-align: center;"| ~30 |
|[[Stellar black hole|Stellar-mass black holes]] ||style="text-align: center;"| ~10 ''M''<sub>[[Sun]]</sub> ||style="text-align: center;"| ~30 km |
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|[[Primordial black hole]]||style="text-align: center;"| up to ~M<sub>[[Moon]]</sub> ||style="text-align: center;"|up to ~0.1 |
|[[Primordial black hole]]||style="text-align: center;"| up to ~''M''<sub>[[Moon]]</sub> ||style="text-align: center;"|up to ~0.1 mm |
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Black holes are commonly classified according to their mass, independent of angular momentum ''J''. The size of a black hole, as determined by the radius of the event horizon, or [[Schwarzschild radius]], is proportional to the mass <math>M\,</math> through <math>r_{sh} \approx 2.95\, M/M_\bigodot \;\mathrm{km,}</math> where <math>r_{sh}\,</math> is the Schwarzschild radius and <math>M_\bigodot</math> is the [[solar mass|mass of the Sun]]. |
Black holes occurring in nature are commonly classified according to their mass, independent of angular momentum ''J''. The size of a black hole, as determined by the radius of the event horizon, or [[Schwarzschild radius]], is proportional to the mass <math>M\,</math> through <math>r_{sh} \approx 2.95\, M/M_\bigodot \;\mathrm{km,}</math> where <math>r_{sh}\,</math> is the Schwarzschild radius and <math>M_\bigodot</math> is the [[solar mass|mass of the Sun]]. Thus, size and mass have a simple relationship, which is [[Rotating black hole|independent of rotation]]. The size (volume) of a black hole is defined by its event horizon, as its true potential volume within the event horizon is indistinguishable. Some physicists contend that black holes are infinitesimally small. According to this mass/size criterion then, black holes are commonly classified as: |
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* [[Supermassive black hole]]s that contain hundreds of thousands to billions of solar masses are believed to exist in the center of most galaxies, including our own [[Milky Way]]. They are thought to be responsible for [[Active galactic nucleus|active galactic nuclei]], and presumably form either from the coalescence of smaller black holes, or by the accretion of stars and gas onto them. The largest known supermassive black hole is located in [[OJ 287]] weighing in at 18 billion solar masses.<ref>{{cite journal |title=A massive binary black-hole system in OJ 287 and a test of general relativity |journal=[[Nature (journal)|Nature]] |year=2008 |date=April 2008 |volume=452 |doi=10.1038/nature06896 |pages=851–853|last1=Valtonen |first1=M. J. |last2=Lehto |first2=H. J. |last3=Nilsson |first3=K. |last4=Heidt |first4=J. |last5=Takalo |first5=L. O. |last6=Sillanpää |first6=A. |last7=Villforth |first7=C. |last8=Kidger |first8=M. |last9=Poyner |first9=G. |last10=Pursimo |first10=T. |last11=Zola |first11=S. |last12=Wu |first12=J.-H. |last13=Zhou |first13=X. |last14=Sadakane |first14=K. |last15=Drozdz |first15=M. |last16=Koziel |first16=D. |last17=Marchev |first17=D. |last18=Ogloza |first18=W. |last19=Porowski |first19=C. |last20=Siwak |first20=M. |last21=Stachowski |first21=G. |last22=Winiarski |first22=M. |last23=Hentunen |first23=V.-P. |last24=Nissinen |first24=M. |last25=Liakos |first25=A. |last26=Dogru |first26=S. |issue=7189 |pmid=18421348 |arxiv=0809.1280 |s2cid=4412396 }}</ref> |
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* [[Supermassive black hole|Supermassive]] - contain hundreds of thousands to billions of solar masses. and are thought to exist in the center of most galaxies,<ref>{{Cite journal |
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* [[Intermediate-mass black hole]]s, whose sizes are measured in thousands of solar masses, probably exist. They have been proposed as a possible power source for the [[ultra-luminous X ray source]]s. There is no known mechanism for them to form directly, so they most probably form via collisions of lower mass black holes, either in the dense stellar cores of [[globular clusters]] or galaxies. Such creation events should produce intense bursts of [[gravitational waves]], which [[LIGO|may be observed]] in the near- to mid-term. The boundary limit between super- and intermediate-mass black holes is a matter of convention. Their lower mass limit, the maximum mass for direct formation of a single black hole from collapse of a massive star, is poorly known at present. |
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| volume = 31 |
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* [[Stellar black hole|Stellar-mass black holes]] have masses ranging from a lower limit of about 1.5–3.0 solar masses (the [[Tolman-Oppenheimer-Volkoff limit]] for the maximum mass of neutron stars) up to perhaps 15–20 solar masses, and are created by the collapse of individual stars, or by the coalescence (inevitable, due to [[gravitational radiation]]) of [[Neutron star#Binary neutron stars|binary neutron stars]]. Stars may form with [[Initial mass function|initial masses]] up to ≈100 solar masses, or possibly even higher, but these shed most of their outer massive layers during earlier phases of their evolution, either blown away in stellar winds during the [[red giant]], [[Asymptotic giant branch|AGB]], and [[Wolf-Rayet]] stages, or expelled in [[supernova]] explosions for stars that turn into neutron stars or black holes. Being known mostly by theoretical models for late-stage stellar evolution, the upper limit for the mass of stellar-mass black holes is somewhat uncertain at present. The cores of still lighter stars form [[white dwarf]]s. |
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| issue = 1 |
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* [[Micro black hole]]s (also '''mini black holes''') have masses much less than that of a star. At these sizes, the effects of [[quantum mechanics]] are expected to come into play. There is no known mechanism for them to form via normal processes of stellar evolution, but certain [[cosmic inflation|inflationary]] scenarios predicted their production during the early stages of the evolution of the universe. According to some theories of [[quantum gravity]] they may also be produced in the highly energetic reaction produced by [[cosmic rays]] hitting the [[atmosphere]] or even in [[particle accelerators]] such as the [[Large Hadron Collider]]. The theory of [[Hawking radiation]] predicts that such black holes will evaporate in bright flashes of [[gamma radiation]]. [[NASA]]'s [[Fermi Gamma-ray Space Telescope]] satellite (formerly GLAST), launched in 2008, will search for such flashes as one of its scientific objectives. |
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| pages = 473–521 |
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| last = Antonucci |
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| first = R. |
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| title = Unified Models for Active Galactic Nuclei and Quasars |
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| journal = Annual Reviews in Astronomy and Astrophysics |
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| date = 1993 |
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| doi = 10.1146/annurev.aa.31.090193.002353 |
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}}</ref><ref>{{Cite journal |
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| volume = 107 |
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| pages = 803–845 |
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| last = Urry |
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| first = C. |
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| coauthors = Paolo Padovani |
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| title = Unified Schemes for Radio-Loud Active Galactic Nuclei |
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| journal = Publications of the Astronomical Society of the Pacific |
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| date = 1995 |
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| doi = 10.1086/133630 |
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}}</ref> including the [[Milky Way]].<ref>{{cite journal |last=Schödel |first=R. |authorlink= |coauthors=''et al.'' |year=2002 |month= |title=A star in a 15.2-year orbit around the supermassive black hole at the centre of the Milky Way |journal=Nature |volume=419 |issue=6908 |pages=694–696 |doi=10.1038/nature01121 |url= |accessdate= |quote= }}</ref> They are believed to be responsible for [[Active galactic nucleus|active galactic nuclei]], and presumably form either from the coalescence of smaller black holes, or by the accretion of stars and gas onto them. The largest known supermassive black hole is located in [[OJ 287]] weighing in at 18 billion solar masses.<ref>{{Citation |last1=Valtonen |first1=M.J. |last2=et al.. |title=A massive binary black-hole system in OJ 287 and a |
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test of general relativity |journal=[[Nature (journal)|Nature]] |year=2008 |volume=452 |doi=10.1038/nature06896 |pages=851}}</ref> |
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==Features== |
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* [[Intermediate-mass black hole|Intermediate]] - contain thousands of solar masses. They have been proposed as a possible power source for [[ultraluminous X-ray source]]s.<ref>{{Citation |last1=Maccarone |first1=T.J. |last2=et al.. |title=A black hole in a globular cluster |journal=[[Nature (journal)|Nature]] |year=2007 |volume=455 |doi=10.1038/nature05434 |pages=183-185}}</ref> There is no known mechanism for them to form directly, so they likely form via collisions of lower mass black holes, either in the dense stellar cores of [[globular clusters]] or galaxies.{{fact}} Such creation events should produce intense bursts of [[gravitational waves]], which [[LIGO|may be observed]] soon. The boundary between super- and intermediate-mass black holes is a matter of convention. Their lower mass limit, the maximum mass for direct formation of a single black hole from collapse of a massive star, is poorly known at present. |
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* [[Stellar black hole|Stellar-mass black holes]] - have masses ranging from a lower limit of about 1.5–3.0 solar masses (the [[Tolman-Oppenheimer-Volkoff limit]] for the maximum mass of neutron stars) up to perhaps 15–20 solar masses. They are created by the collapse of individual stars, or by the coalescence (inevitable, due to [[gravitational radiation]]) of [[Neutron star#Binary neutron stars|binary neutron stars]]. Stars may form with [[Initial mass function|initial masses]] up to ≈100 solar masses, or possibly even higher, but these shed most of their outer massive layers during earlier phases of their evolution, either blown away in stellar winds during the [[red giant]], [[Asymptotic giant branch|AGB]], and [[Wolf-Rayet]] stages, or expelled in [[supernova]] explosions for stars that turn into neutron stars or black holes. Being known mostly by theoretical models for late-stage stellar evolution, the upper limit for the mass of stellar-mass black holes is somewhat uncertain at present. The cores of still lighter stars form [[white dwarf]]s. |
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* [[Micro black hole|Micro]] (also '''mini black holes''') - have masses much less than that of a star. At these sizes, the effects of [[quantum mechanics]] are expected to come into play. There is no known mechanism for them to form via normal processes of stellar evolution, but certain [[cosmic inflation|inflationary]] scenarios predict their production during the early stages of the evolution of the universe.{{fact}} According to some theories of [[quantum gravity]] they may also be produced in the highly energetic reaction produced by [[cosmic rays]] hitting the [[atmosphere]] or even in [[particle accelerators]] such as the [[Large Hadron Collider]].{{fact}} The theory of [[Hawking radiation]] predicts that such black holes will evaporate in bright flashes of [[gamma radiation]]. [[NASA]]'s [[Fermi Gamma-ray Space Telescope]] satellite (formerly GLAST) launched in 2008 is searching for such flashes.<ref>{{cite web |url=http://www.nasa.gov/mission_pages/GLAST/news/glast_gbm.html |title=NASA's GLAST Burst Monitor Team Hard at Work Fine-Tuning Instrument and Operations |publisher=NASA |date=2008-07-28}}</ref> |
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===Event horizon=== |
===Event horizon=== |
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{| align="right" class="wikitable" style="margin:1ex 1ex 1ex 1ex" width="400" |
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|[[Image:BH-no-escape-1.svg]]<br/>Far away from the black hole a particle can move in any direction. It is only restricted by the speed of light. |
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|[[Image:BH-no-escape-2.svg]]<br/>Closer to the black hole spacetime starts to deform. There are more paths going towards the black hole than paths moving away. |
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|[[Image:BH-no-escape-3.svg]]<br/>Inside of the event horizon all paths bring the particle closer to the center of the black hole. It is no longer possible for the particle to escape. The diagrams here are effectively Finkelstein diagrams using an advanced time parameter.<ref>{{cite book |first=Stephen W. |last=Hawking |coauthors=[[George Ellis]] |title=The large scale structure of space-time |publisher=[[Cambridge University Press]] |location=[[Cambridge]] |year=1973 |page=[http://books.google.com/books?id=QagG_KI7Ll8C&pg=PA152 152] |isbn=0-521-09906-4 |oclc=16002677}}</ref> |
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{{main|Event horizon}} |
{{main|Event horizon}} |
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The defining feature of a black hole is the event horizon, a surface in [[spacetime]] that marks a point of no return. Once an object crosses this surface, it cannot return to the other side. Consequently, anything inside this surface is completely hidden from outside observers. Other than this, the event horizon is a completely normal part of space with no special features that would allow someone falling into the black hole to know when they would cross the horizon. The event horizon is not a solid surface, and does not obstruct or slow down matter or radiation that is traveling towards the region within the event horizon. |
The defining feature of a black hole is the event horizon, a surface in [[spacetime]] that marks a point of no return. Once an object crosses this surface, it cannot return to the other side. Consequently, anything inside this surface is completely hidden from outside observers. Other than this, the event horizon is a completely normal part of space with no special features that would allow someone falling into the black hole to know when they would cross the horizon. The event horizon is not a solid surface, and does not obstruct or slow down matter or radiation that is traveling towards the region within the event horizon. |
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===Singularity=== |
===Singularity=== |
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{{main|Gravitational singularity}} |
{{main|Gravitational singularity}} |
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According to [[general relativity]], there is a space-time ''singularity'' at the center of a spherical black hole, which means an infinite space-time curvature. It means that, from the |
According to [[general relativity]], there is a space-time ''singularity'' at the center of a spherical black hole, which means an infinite space-time curvature. It means that, from the viewpoint of an observer falling into a black hole, in a finite time (at the end of his fall) a black hole's mass becomes entirely compressed into a region with zero volume, so its density becomes [[Infinity|infinite]]. This zero-volume, infinitely dense region at the center of a black hole is called a [[gravitational singularity]]. |
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The singularity in a non-rotating black hole is a point, in other words it has zero length, width, and height. The singularity of a [[rotating black hole]] is smeared out to form a [[ring singularity|ring shape]] lying in the plane of rotation. The ring still has no thickness and hence no volume. |
The singularity in a non-rotating black hole is a point, in other words it has zero length, width, and height. The singularity of a [[rotating black hole]] is smeared out to form a [[ring singularity|ring shape]] lying in the plane of rotation. The ring still has no thickness and hence no volume. |
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The appearance of singularities in general relativity is commonly perceived as signaling the breakdown of the theory. This breakdown is not unexpected, as it occurs in a situation where [[quantum mechanics|quantum mechanical]] effects should become important, since densities are high and particle interactions should thus play a role. |
The appearance of singularities in general relativity is commonly perceived as signaling the breakdown of the theory. This breakdown is not unexpected, as it occurs in a situation where [[quantum mechanics|quantum mechanical]] effects should become important, since densities are high and particle interactions should thus play a role. Unfortunately, to date it has not been possible to combine quantum and gravitation effects in a single theory. It is however quite generally expected that a theory of [[quantum gravity]] will feature black holes without singularities. |
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Formation of the singularity takes a finite (and very short) time only from the viewpoint of an infalling observer. From the standpoint of a distant observer, it takes infinite time to do so due to [[gravitational time dilation]]. |
Formation of the singularity takes a finite (and very short) time only from the viewpoint of an infalling observer. From the standpoint of a distant observer, it takes infinite time to do so due to [[gravitational time dilation]]. |
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Other [[compact object]]s, such as [[neutron stars]], can also have photon spheres.<ref> |
Other [[compact object]]s, such as [[neutron stars]], can also have photon spheres.<ref> |
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{{ |
{{cite journal |first=Robert J. |last=Nemiroff |title=Visual distortions near a neutron star and black hole |journal= [[American Journal of Physics]] |volume=61 |issue=7 |pages=619–632 |year=1993 |date=July 1993 |doi=10.1119/1.17224|arxiv=astro-ph/9312003 |s2cid=16640860 }}</ref> This follows from the fact gravitation field of an object does not depend on its actual size, hence any object that is smaller than 1.5 times the Schwarzschild radius corresponding to its mass will in fact have a photon sphere. |
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===Ergosphere=== |
===Ergosphere=== |
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[[ |
[[File:Ergosphere of a rotating black hole.svg|thumb|right|250px|ergosphere of a rotating black hole|The ergosphere is an oblate spheroid region outside of the event horizon, where objects cannot remain stationary.]] |
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{{main|Ergosphere}} |
{{main|Ergosphere}} |
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Rotating black holes are surrounded by a region of spacetime in which it is impossible to stand still, called the ergosphere. This is the result of a process known as [[frame-dragging]]; general relativity predicts that any rotating mass will tend to slightly "drag" along the spacetime immediately surrounding it. Any object near the rotating mass will tend to start moving in the direction of rotation. For a rotating black hole this effect becomes so strong near the event horizon that an object would have to move faster than the speed of light in the opposite direction to just stand still. |
Rotating black holes are surrounded by a region of spacetime in which it is impossible to stand still, called the ergosphere. This is the result of a process known as [[frame-dragging]]; general relativity predicts that any rotating mass will tend to slightly "drag" along the spacetime immediately surrounding it. Any object near the rotating mass will tend to start moving in the direction of rotation. For a rotating black hole this effect becomes so strong near the event horizon that an object would have to move faster than the speed of light in the opposite direction to just stand still. |
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Objects and radiation can also ''escape'' from the ergosphere. In fact the [[Penrose process]] predicts that objects will sometimes fly out of the ergosphere, obtaining the energy for this by "stealing" some of the black hole's rotational energy. If a large total mass of objects escapes in this way, the black hole will spin more slowly and may even stop spinning eventually. |
Objects and radiation can also ''escape'' from the ergosphere. In fact the [[Penrose process]] predicts that objects will sometimes fly out of the ergosphere, obtaining the energy for this by "stealing" some of the black hole's rotational energy. If a large total mass of objects escapes in this way, the black hole will spin more slowly and may even stop spinning eventually. |
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===Hawking radiation=== |
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{{main|Hawking radiation}} |
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In 1974, [[Stephen Hawking]] showed that black holes are not entirely black but emit small amounts of thermal radiation.<ref name=Hawking1974>{{cite journal |last=Hawking |first=S.W. |title=Black hole explosions? |journal=Nature |year=1974 |volume=248 |issue=5443 |pages=30–31 |url=http://www.nature.com/nature/journal/v248/n5443/abs/248030a0.html |doi=10.1038/248030a0|s2cid=4290107 }}</ref> He got this result by applying [[quantum field theory]] in a static black hole background. The result of his calculations is that a black hole should emit particles in a perfect [[black body spectrum]]. This effect has become known as [[Hawking radiation]]. Since Hawking's result many others have verified the effect through various methods.<ref>{{cite journal |arxiv=hep-th/0409024 |doi=10.1088/1367-2630/7/1/203 |title=Hawking radiation and black hole thermodynamics |year=2005 |author=Page, Don N |journal=New Journal of Physics |volume=7 |pages=203|s2cid=119047329 }}</ref> |
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The temperature of the emitted black body spectrum is proportional to the [[surface gravity]] of the black hole. For a Schwarzschild black hole this is inversely proportional to the mass. Consequently, large black holes are very cold and emit very little radiation. A stellar black hole of 10 solar masses, for example, would have a [[Hawking temperature]] of several [[nanokelvin]]s, much less than the 2.7 K produced by the [[cosmic microwave background]]. Micro black holes on the other hand could be quite bright producing high energy gamma rays. |
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Due to low Hawking temperature of stellar black holes, Hawking radiation has never been observed at any of the black hole candidates. |
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==Effects of falling into a black hole== |
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This section describes what happens when something falls into a Schwarzschild (i.e. non-rotating and uncharged) black hole. Rotating and charged black holes have some additional complications when falling into them, which are not treated here. |
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===Spaghettification=== |
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{{main|Spaghettification}} |
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An object in any very strong gravitational field feels a [[tidal force]] stretching it in the direction of the object generating the gravitational field. This is because the [[inverse square law]] causes nearer parts of the stretched object to feel a stronger attraction than farther parts. Near black holes, the tidal force is expected to be strong enough to deform any object falling into it, even atoms or composite [[nucleon]]s; this is called spaghettification. |
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The strength of the tidal force of a black hole depends on how gravitational attraction changes with distance, rather than on the absolute force being felt. This means that small black holes cause spaghettification while infalling objects are still outside their event horizons, whereas objects falling into large, supermassive black holes may not be deformed or otherwise feel excessively large forces before passing the event horizon. |
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===Before the falling object crosses the event horizon=== |
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An object in a gravitational field experiences a slowing down of [[time]], called [[gravitational time dilation]], relative to observers outside the field. The outside observer will see that physical processes in the object, including clocks, appear to run slowly. As a test object approaches the event horizon, its gravitational time dilation (as measured by an observer far from the hole) would approach infinity. Its time would appear to be stopped. |
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From the viewpoint of a distant observer, an object falling into a black hole appears to slow down, approaching but never quite reaching the event horizon: and it appears to become redder and dimmer, because of the extreme [[gravitational red shift]] caused by the gravity of the black hole. Eventually, the falling object becomes so dim that it can no longer be seen, at a point just before it reaches the event horizon. All of this is a consequence of time dilation: the object's movement is one of the processes that appear to run slower and slower, and the time dilation effect is more significant than the acceleration due to gravity; the [[frequency]] of light from the object appears to decrease, making it look redder, because the light appears to complete fewer cycles per "tick" of the ''observer's'' clock; lower-frequency light has less energy and therefore appears dimmer, as well as redder. |
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From the viewpoint of the falling object, distant objects generally appear [[Blue shift|blue-shifted]] due to the gravitational field of the black hole. This effect may be partly (or even entirely) negated by the [[Redshift|red shift]] caused by the velocity of the infalling object with respect to the object in the distance. |
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===As the object passes through the event horizon=== |
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From the viewpoint of the falling object, nothing particularly special happens at the event horizon. In fact, there is no (local) way for him to find out whether he has passed the horizon or not. An infalling object takes a finite [[proper time]] (i.e. measured by its own clock) to fall past the event horizon. This in contrast with the infinite amount of time it takes for a distant observer to see the infalling object cross the horizon. |
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===Inside the event horizon=== |
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The object reaches the singularity at the center within a finite amount of [[proper time]], as measured by the falling object. An observer on the falling object would continue to see objects outside the event horizon, [[Blue shift|blue-shifted]] or [[Redshift|red-shifted]] depending on the falling object's trajectory. |
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The amount of proper time a faller experiences below the event horizon depends upon where they started from rest, with the maximum being for someone who starts from rest at the event horizon. A paper in 2007 examined the effect of firing a rocket pack within the black hole, showing that this can only reduce the proper time of a person who starts from rest at the event horizon. However, for anyone else, a judicious burst of the rocket can extend the lifetime of the faller, but overdoing it will again reduce the proper time experienced. However, this cannot prevent the inevitable collision with the central singularity.<ref>{{ |
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cite journal |
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|bibcode=2007PASA...24...46L|doi=10.1071/AS07012 |
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|author=Lewis, G. F. and Kwan, J. |
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|year=2007 |
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|title=No Way Back: Maximizing Survival Time Below the Schwarzschild Event Horizon |
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|journal=Publications of the Astronomical Society of Australia |
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|volume=24 |
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|issue=2 |
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|pages=46–52 |
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|arxiv=0705.1029 |
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|s2cid=17261076 |
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}}</ref> |
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===Hitting the singularity=== |
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As an infalling object approaches the singularity, [[tidal force]]s acting on it approach infinity. All components of the object, including [[atom]]s and [[subatomic particles]], are torn away from each other before striking the singularity. At the singularity itself, effects are unknown; it is believed that a theory of [[quantum gravity]] is needed to accurately describe events near it.<!-- Regardless, as soon as an object passes within the hole's event horizon, it is lost to the outside universe. An observer far from the hole simply sees the hole's mass, charge, and angular momentum change slightly, to reflect the addition of the infalling object's matter. After the event horizon all is unknown. Anything that passes this point cannot be retrieved to study. -- commented out since nothing "passes within the hole's event horizon and lost to the outside universe" in finite time as outside universe sees it. For outside universe, a rock thrown into the hole one million years ago is still outside of the horizon and, theoretically, can be retrieved. --> |
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<!--==Black hole parameters== |
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Astrophysical black holes are characterized by two parameters: their mass and their angular momentum (or spin). The mass parameter ''M'' is equivalent to a characteristic length ''GM/c<sup>2</sup>=1.48 km(M/M<sub>0</sub>)'' , or a characteristic timescale'' GM/c³=4.93 x 10<sup>-6</sup>(M/M<sub>0</sub>)'' , where ''M<sub>0</sub>'' denotes the mass of the Sun. These scales, for example, give the order of magnitude of the radii and periods of near-hole orbits. The timescale also applies to the process in which a developing horizon settles into its asymptotically stationary form. For a stellar mass hole this is of order 10<sup>-5</sup> sec , while for a supermassive hole of 10<sup>8</sup> ''M<sub>0</sub>'' , it is thousands of seconds. |
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For Schwarzschild holes, and approximately for Kerr holes, the horizon is at radius ''R<sub>H</sub>=2GM/c²''. |
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At the horizon the "acceleration of gravity" has no meaning, since a falling observer cannot stop at the horizon to be weighed. What is relevant at the horizon is the tidal stresses that stretch and distort the falling observer. This tidal stretching is given by the same expression, the gradient of the gravitational acceleration, as in Newtonian theory: |
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''2GM/R<sub>H</sub><sup>3</sup>=c<sup>6</sup>/(4G<sup>2</sup>M<sup>2</sup>)'' . |
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In the case of a solar mass black hole the tidal stress (acceleration per unit length) is enormous at the horizon, on the order of : '' 3 x 10<sup>9</sup>(M/M<sub>0</sub>)<sup>2</sup> sec<sup>-2</sup>'' : that is, a person would experience a differential gravitational field of about ''10<sup>9</sup>'' Earth gravities, enough to rip apart ordinary materials. For a supermassive hole, by contrast, the tidal force at the horizon is smaller by a typical factor 10<sup>10-16</sup> and would be easily survivable. However, at the central singularity, deep inside the event horizon, the tidal stress is infinite. |
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In addition to its mass ''M'', the Kerr spacetime is described with a spin parameter 'a' defined by the dimensionless expression ''a/M= cJ/GM<sup>2</sup>'' |
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where ''J'' is the angular momentum of the hole. For the Sun (based on surface rotation) this number is about 0.2, and is much larger for many stars. Since angular momentum is ubiquitous in astrophysics, and since it is expected to be approximately conserved during collapse and black hole formation, astrophysical holes are expected to have significant values of ''a/M'' , from several tenths up to and approaching unity. |
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The value of ''a/M'' can be unity (an "extreme" Kerr hole), but it cannot be greater than unity. In the mathematics of general relativity, exceeding this limit replaces the event horizon with an inner boundary on the spacetime where tidal forces become infinite. Because this singularity is "visible" to observers, rather than hidden behind a horizon, as in a black hole, it is called a naked singularity. Toy models and heuristic arguments suggest that as ''a/M'' approaches unity it becomes more and more difficult to add angular momentum. The conjecture that such mechanisms will always keep ''a/M'' below unity is called cosmic censorship. |
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The inclusion of angular momentum changes details of the description of the horizon, so that, for example, the horizon area becomes ''Horizon area= 4πG<sup>2</sup>/c<sup>4</sup>[{M+(M²-a²)<sup>1/2</sup>}²+a²]'' |
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This modification of the Schwarzschild (''a''=0) result is not significant until ''a/M'' becomes very close to unity. For this reason, good estimates can be made in many astrophysical scenarios with ''a'' ignored.--> |
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==Formation and evolution== |
==Formation and evolution== |
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From the exotic nature of black holes, it is natural to question if such bizarre objects could actually exist in nature or that they are merely pathological solutions to Einstein's equations. However in 1970, Hawking and Penrose proved the opposite; under generic conditions black holes are expected to form in any universe.<ref name=HawkingPenrose1970>{{cite journal |doi=10.1098/rspa.1970.0021 |url=http://rspa.royalsocietypublishing.org/content/314/1519/529.abstract |first=Stephen |last=Hawking |authorlink=Stephen Hawking |coauthors=[[Roger Penrose]] | |
From the exotic nature of black holes, it is natural to question if such bizarre objects could actually exist in nature or that they are merely pathological solutions to Einstein's equations. However in 1970, Hawking and Penrose proved the opposite; under generic conditions black holes are expected to form in any universe.<ref name=HawkingPenrose1970>{{cite journal |doi=10.1098/rspa.1970.0021 |url=http://rspa.royalsocietypublishing.org/content/314/1519/529.abstract |first=Stephen |last=Hawking |authorlink=Stephen Hawking |coauthors=[[Roger Penrose]] |date=January 1970 |title=The Singularities of Gravitational Collapse and Cosmology |journal=[[Proceedings of the Royal Society#Proceedings of the Royal Society A|Proceedings of the Royal Society A]] |volume=314 |issue=1519 |pages=529–548|s2cid=120208756 }}</ref> The primary formation process for black holes is expected to be the [[gravitational collapse]] of heavy objects such as stars, but there are also more exotic processes that can lead to the production of black holes. |
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=== |
===Gravitation collapse=== |
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{{main|Gravitational collapse}} |
{{main|Gravitational collapse}} |
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=====Creation of primordial black holes in the big bang===== |
=====Creation of primordial black holes in the big bang===== |
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Gravitational collapse requires great densities. In the current epoch of the universe these high densities are only found in stars, but in the early universe shortly after the [[big bang]] densities were much greater, possibly allowing for the creation of black holes. The high density alone is not enough to allow the formation of black holes since a uniform mass distribution will not allow the mass to bunch up. In order for [[primordial black holes]] to form in such a dense medium, there must be initial density perturbations which can then grow under their own gravity. Different models for the early universe vary widely in their predictions of the size of these perturbations. Various models predict the creation of black holes, ranging from a [[Planck mass]] to hundreds of thousands of solar masses.<ref>{{cite arXiv |eprint=astro-ph/ |
Gravitational collapse requires great densities. In the current epoch of the universe these high densities are only found in stars, but in the early universe shortly after the [[big bang]] densities were much greater, possibly allowing for the creation of black holes. The high density alone is not enough to allow the formation of black holes since a uniform mass distribution will not allow the mass to bunch up. In order for [[primordial black holes]] to form in such a dense medium, there must be initial density perturbations which can then grow under their own gravity. Different models for the early universe vary widely in their predictions of the size of these perturbations. Various models predict the creation of black holes, ranging from a [[Planck mass]] to hundreds of thousands of solar masses.<ref>{{cite arXiv |eprint=astro-ph/0511743 |last1=Carr | first1=B. J. |title=Primordial Black Holes: Do They Exist and Are They Useful? |class=astro-ph |year=2005}}</ref> Primordial black holes could thus account for the creation of any type of black hole. |
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=== |
===Production in high energy collisions=== |
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Gravitational collapse is not the only process that could create black holes. In principle, black holes could also be created in high energy collisions that create sufficient density. Since classically black holes can take any mass, one would expect [[micro black hole]]s to be created in any such process no matter how low the energy. However, to date, no such events have ever been detected either directly or indirectly as a deficiency of the mass balance in [[particle accelerator]] experiments.<ref>{{cite journal |doi=10.1103/PhysRevD.65.056010 |arxiv=hep-ph/0106219 |title=High energy colliders as black hole factories: The end of short distance physics |year=2002 |author=Giddings, Steven B. |journal=Physical Review D |volume=65 |issue=5 |pages=056010|s2cid=1203487 }}</ref> This suggests that there must be a lower limit for the mass of black holes. |
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[[Image:CMS Higgs-event.jpg|thumb|right|A simulated event in the CMS detector, a collision in which a micro black hole may be created.]] |
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Gravitational collapse is not the only process that could create black holes. In principle, black holes could also be created in high energy collisions that create sufficient density. Since classically black holes can take any mass, one would expect [[micro black hole]]s to be created in any such process no matter how low the energy. However, to date, no such events have ever been detected either directly or indirectly as a deficiency of the mass balance in [[particle accelerator]] experiments.<ref>{{cite journal |doi=10.1103/PhysRevD.65.056010 |id={{arXiv|archive=hep-ph|id=0106219v4}} |title=High energy colliders as black hole factories: The end of short distance physics |year=2002 |author=Giddings, Steven B. |journal=Physical Review D |volume=65 |pages=056010}}</ref> This suggests that there must be a lower limit for the mass of black holes. |
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Theoretically this boundary is expected to lie around the [[Planck mass]] (~10<sup>19</sup> [[GeV]]/c<sup>2</sup>), where quantum effects are expected to make the theory of general relativity break down completely.{{ |
Theoretically this boundary is expected to lie around the [[Planck mass]] (~10<sup>19</sup> [[GeV]]/c<sup>2</sup>), where quantum effects are expected to make the theory of general relativity break down completely.{{Citation needed|date=June 2008}} This would put the creation of black holes firmly out of reach of any high energy process occurring on or near the Earth. Certain developments in quantum gravity however suggest that this bound could be much lower. Some [[braneworld]] scenarios for example put the Planck mass much lower, may be even as low as 1 TeV.<ref>{{cite journal |arxiv=hep-ph/9803315 |doi=10.1016/S0370-2693(98)00466-3 |title=The hierarchy problem and new dimensions at a millimeter |year=1998 |author=Arkani–Hamed, N |journal=Physics Letters B |volume=429 |issue=3–4 |pages=263–272|s2cid=15903444 }}</ref> This would make it possible for micro black holes to be created in the high energy collisions occurring when cosmic rays hit the Earth's atmosphere, or even maybe in the new [[Large Hadron Collider]] at [[CERN]]. These theories are however very speculative, and the creation of black holes in these processes is deemed unlikely by many specialists. |
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===Growth=== |
===Growth=== |
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===Evaporation=== |
===Evaporation=== |
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If Hawking's theory of black hole radiation is correct then black holes are expected to emit a thermal spectrum of radiation, and thereby lose mass, because according to the theory of relativity mass is just highly condensed energy (''E'' = ''mc''<sup>2</sup>).<ref name=Hawking1974/> Black holes will thus shrink and evaporate over time. The temperature of this spectrum ([[Hawking temperature]]) is proportional to the [[surface gravity]] of the black hole, which in turn is inversely proportional to the mass. Large black holes thus emit less radiation than small black holes. |
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{{main|Hawking radiation}} |
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In 1974, [[Stephen Hawking]] showed that black holes are not entirely black but emit small amounts of thermal radiation.<ref name=Hawking1974>{{Citation|last=Hawking |first=S.W. |title=Black hole explosions? |journal=Nature |year=1974 |volume=248 |pages=30–31 |url=http://www.nature.com/nature/journal/v248/n5443/abs/248030a0.html |doi=10.1038/248030a0}}</ref>He got this result by applying [[quantum field theory]] in a static black hole background. The result of his calculations is that a black hole should emit particles in a perfect [[black body spectrum]]. This effect has become known as [[Hawking radiation]]. Since Hawking's result many others have verified the effect through various methods.<ref>{{cite journal |id={{arXiv|archive=hep-th|id=0409024v3}} |doi=10.1088/1367-2630/7/1/203 |title=Hawking radiation and black hole thermodynamics |year=2005 |author=Page, Don N |journal=New Journal of Physics |volume=7 |pages=203}}</ref>If his theory of black hole radiation is correct then black holes are expected to emit a thermal spectrum of radiation, and thereby lose mass, because according to the theory of relativity mass is just highly condensed energy (''E'' = ''mc''<sup>2</sup>).<ref name=Hawking1974/> Black holes will shrink and evaporate over time. The temperature of this spectrum ([[Hawking temperature]]) is proportional to the [[surface gravity]] of the black hole, which in turn is inversely proportional to the mass. Large black holes, therefore, emit less radiation than small black holes. |
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A stellar black hole of 5 solar masses has a Hawking temperature of about 12 nanokelvins. This is far less than the 2.7 K produced by the cosmic microwave background. Stellar mass (and larger) black holes thus receive more mass from the CMB than they emit through Hawking radiation and will thus grow instead of shrink. In order to have a Hawking temperature larger than 2.7 K (and thus be able to evaporate) a black hole needs to be lighter than the [[Moon]] (and thus have diameter of less than a tenth of a millimeter). |
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On the other hand if a black hole is very small the radiation effects are expected to become very strong. Even a black hole that is heavy compared to a human would evaporate in an instant. A black hole the weight of a car (~10<sup>−24</sup> m) would only take a nanosecond to evaporate, during which time it would briefly have a luminosity more than 200 times that of the sun. Lighter black holes are expected to evaporate even faster, for example a black hole of mass 1 TeV/''c''<sup>2</sup> would take less than 10<sup>−88</sup> seconds to evaporate completely. Of course, for such a small black hole [[quantum gravity|quantum gravitation]] effects are expected to play an important role and could even{{spaced ndash}}although current developments in quantum gravity do not indicate so{{spaced ndash}}hypothetically make such a small black hole stable. |
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A stellar black hole of 5 solar masses has a Hawking temperature of about 12 nanokelvins. This is far less than the 2.7 K produced by the [[cosmic microwave background]]. Stellar mass (and larger) black holes receive more mass from the cosmic microwave background than they emit through Hawking radiation and will thus grow instead of shrink. In order to have a Hawking temperature larger than 2.7 K (and be able to evaporate) a black hole needs to be lighter than the [[Moon]] (and therefore a diameter of less than a tenth of a millimeter). |
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==Techniques for finding black holes== |
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On the other hand if a black hole is very small, the radiation effects are expected to become very strong. Even a black hole that is heavy compared to a human would evaporate in an instant. A black hole the weight of a car (~10<sup>-24</sup> m) would only take a nanosecond to evaporate, during which time it would briefly have a luminosity more than 200 times that of the sun. Lighter black holes are expected to evaporate even faster, for example a black hole of mass 1 TeV/''c''<sup>2</sup> would take less than 10<sup>-88</sup> seconds to evaporate completely. Of course, for such a small black hole [[quantum gravity|quantum gravitation]] effects are expected to play an important role and could even{{ndash}} although current developments in quantum gravity do not indicate so{{ndash}} hypothetically make such a small black hole stable |
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==Observation== |
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===Accretion disks and gas jets=== |
===Accretion disks and gas jets=== |
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[[ |
[[File:Black hole jet diagram.jpg|left|thumb|Formation of extragalactic jets from a black hole's [[Accretion disc|accretion disk]]]] |
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Most [[Accretion disc|accretion disks]] and [[Relativistic jet|gas jets]] are not clear proof that a [[stellar-mass black hole]] is present, because other massive, ultra-dense objects such as [[neutron star]]s and [[white dwarf]]s cause accretion disks and gas jets to form and to behave in the same ways as those around black holes. But they can often help by telling astronomers where it might be worth looking for a black hole. |
Most [[Accretion disc|accretion disks]] and [[Relativistic jet|gas jets]] are not clear proof that a [[stellar-mass black hole]] is present, because other massive, ultra-dense objects such as [[neutron star]]s and [[white dwarf]]s cause accretion disks and gas jets to form and to behave in the same ways as those around black holes. But they can often help by telling astronomers where it might be worth looking for a black hole. |
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===Strong radiation emissions=== |
===Strong radiation emissions=== |
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[[File:Black hole quasar NASA.jpg|thumb|right|A "Quasar" Black Hole.]] |
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Steady [[X-ray]] and [[gamma ray]] emissions also do not prove that a black hole is present, but can tell astronomers where it might be worth looking for one - and they have the advantage that they pass fairly easily through [[nebula]]e and gas clouds. |
Steady [[X-ray]] and [[gamma ray]] emissions also do not prove that a black hole is present, but can tell astronomers where it might be worth looking for one - and they have the advantage that they pass fairly easily through [[nebula]]e and gas clouds. |
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But strong, irregular emissions of [[X-ray]]s, [[gamma ray]]s and other [[electromagnetic radiation]] can help to prove that a massive, ultra-dense object is ''not'' a black hole, so that "black hole hunters" can move on to some other object. Neutron stars and other very dense stars have surfaces, and matter colliding with the surface at a high percentage of the speed of light will produce intense flares of radiation at irregular intervals. Black holes have no material surface, so the absence of irregular flares around a massive, ultra-dense object suggests that there is a good chance of finding a black hole there. |
But strong, irregular emissions of [[X-ray]]s, [[gamma ray]]s and other [[electromagnetic radiation]] can help to prove that a massive, ultra-dense object is ''not'' a black hole, so that "black hole hunters" can move on to some other object. Neutron stars and other very dense stars have surfaces, and matter colliding with the surface at a high percentage of the speed of light will produce intense flares of radiation at irregular intervals. Black holes have no material surface, so the absence of irregular flares around a massive, ultra-dense object suggests that there is a good chance of finding a black hole there. |
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Intense but one-time [[gamma ray burst]]s (GRBs) may signal the birth of "new" black holes, because astrophysicists think that GRBs are caused either by the [[gravitational collapse]] of giant stars<ref>{{cite journal | |
Intense but one-time [[gamma ray burst]]s (GRBs) may signal the birth of "new" black holes, because astrophysicists think that GRBs are caused either by the [[gravitational collapse]] of giant stars<ref>{{cite journal |arxiv=astro-ph/0010176 |doi=10.1086/338893 |title=The Observed Offset Distribution of Gamma-Ray Bursts from Their Host Galaxies: A Robust Clue to the Nature of the Progenitors |year=2002 |author=Bloom, J. S. |journal=The Astronomical Journal |volume=123 |issue=3 |pages=1111–1148|s2cid=6939747 }}</ref> or by collisions between neutron stars,<ref name = "Harvard.edu-NeutronStars">{{ |
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cite journal |
cite journal |
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| |
|bibcode=1984SvAL...10..177B|author=Blinnikov, S., ''et al.'' |
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|author=Blinnikov, S., ''et al.'' |
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|year=1984 |
|year=1984 |
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|title=Exploding Neutron Stars in Close Binaries |
|title=Exploding Neutron Stars in Close Binaries |
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|volume=10 |
|volume=10 |
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|pages=177 |
|pages=177 |
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|arxiv=1808.05287 |
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}}</ref> and both types of event involve sufficient mass and pressure to produce black holes. But it appears that a collision between a neutron star and a black hole can also cause a GRB,<ref>{{cite journal |doi=10.1086/154860 |title=The tidal disruption of neutron stars by black holes in close binaries |year=1976 |author=Lattimer, J. M. |journal=The Astrophysical Journal |volume=210 |pages=549}}</ref> so a GRB is not proof that a "new" black hole has been formed. |
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}}</ref> and both types of event involve sufficient mass and pressure to produce black holes. But it appears that a collision between a neutron star and a black hole can also cause a GRB,<ref>{{cite journal |doi=10.1086/154860 |title=The tidal disruption of neutron stars by black holes in close binaries |year=1976 |author=Lattimer, J. M. |journal=The Astrophysical Journal |volume=210 |pages=549|hdl=2152/35059 }}</ref> so a GRB is not proof that a "new" black hole has been formed. |
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All known GRBs come from outside our own galaxy, and most come from billions of [[light year]]s away<ref>{{cite journal |id={{arXiv|archive=astro-ph|id=9505096}} |doi=10.1086/133674 |journal=[[Publications of the Astronomical Society of the Pacific]] |title=How Far Away Are Gamma-Ray Bursters? |first=Bohdan |last=Paczynski |authorlink=Bohdan Paczyński |volume=107 |year=1995 |pages=1167}}</ref> so the black holes associated with them are actually billions of years old. |
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All known GRBs come from outside our own galaxy, and most come from billions of [[light year]]s away<ref>{{cite journal |arxiv=astro-ph/9505096 |doi=10.1086/133674 |journal=[[Publications of the Astronomical Society of the Pacific]] |title=How Far Away Are Gamma-Ray Bursters? |first=Bohdan |last=Paczynski |authorlink=Bohdan Paczyński |volume=107 |year=1995 |pages=1167|s2cid=15952977 }}</ref> so the black holes associated with them are actually billions of years old. |
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Some astrophysicists believe that some [[ultraluminous X-ray source]]s may be the [[Accretion disc|accretion disks]] of [[intermediate-mass black hole]]s.<ref>{{cite journal | |
Some astrophysicists believe that some [[ultraluminous X-ray source]]s may be the [[Accretion disc|accretion disks]] of [[intermediate-mass black hole]]s.<ref>{{cite journal |arxiv=astro-ph/0512480 |doi=10.1086/506579 |title=''XMM-Newton'' Archival Study of the Ultraluminous X-Ray Population in Nearby Galaxies |year=2006 |author=Winter, Lisa M. |journal=The Astrophysical Journal |volume=649 |issue=2 |pages=730–752|s2cid=118445260 }}</ref> |
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[[Quasars]] are thought to be the accretion disks of [[supermassive black hole]]s, since no other known object is powerful enough to produce such strong emissions. Quasars produce strong emission across the [[electromagnetic spectrum]], including [[UV]], [[X-rays]] and [[gamma-rays]] and are visible at tremendous distances due to their high [[luminosity]]. Between 5 and 25% of quasars are "radio loud," so called because of their powerful [[radio]] emission.<ref>{{cite journal | |
[[Quasars]] are thought to be the accretion disks of [[supermassive black hole]]s, since no other known object is powerful enough to produce such strong emissions. Quasars produce strong emission across the [[electromagnetic spectrum]], including [[UV]], [[X-rays]] and [[gamma-rays]] and are visible at tremendous distances due to their high [[luminosity]]. Between 5 and 25% of quasars are "radio loud," so called because of their powerful [[radio]] emission.<ref>{{cite journal |arxiv=astro-ph/0611453 |doi=10.1086/510831 |title=The Radio-Loud Fraction of Quasars is a Strong Function of Redshift and Optical Luminosity |year=2007 |author=Jiang, Linhua |journal=The Astrophysical Journal |volume=656 |issue=2 |pages=680–690|s2cid=15964836 }}</ref> |
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===Gravitational lensing=== |
===Gravitational lensing=== |
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[[File:Black hole lensing web.gif|170px|left|thumb|Simulation of [[Gravitational lensing]] by a black hole which distorts a [[galaxy]] in the background.]] |
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A [[gravitational lens]] is formed when the light from a very distant, bright source (such as a [[quasar]]) is "bent" around a massive object (such as a black hole) between the source object and the observer. The process is known as '''gravitational lensing''', and is one of the [[tests of general relativity|predictions]] of the general theory of relativity. According to this theory, [[mass]] "warps" [[space-time]] to create [[gravitational field]]s and therefore bend [[light]] as a result. |
A [[gravitational lens]] is formed when the light from a very distant, bright source (such as a [[quasar]]) is "bent" around a massive object (such as a black hole) between the source object and the observer. The process is known as '''gravitational lensing''', and is one of the [[tests of general relativity|predictions]] of the general theory of relativity. According to this theory, [[mass]] "warps" [[space-time]] to create [[gravitational field]]s and therefore bend [[light]] as a result. |
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===Objects orbiting possible black holes=== |
===Objects orbiting possible black holes=== |
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{{See also|Kepler problem in general relativity}} |
{{See also|Kepler problem in general relativity}} |
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[[Image:Cygx1 spectrum.jpg|thumb|right|230px|A [[Chandra X-ray Observatory|Chandra]] X-ray spectrum of Cygnus X-1 showing a characteristic peak near 6.4 [[Electron volt|keV]] due to [[ion]]ized [[iron]] in the accretion disk, but the peak is gravitationally red-shifted, broadened by the [[Doppler effect]], and skewed toward lower energies.<ref>{{cite web |
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| author=Staff | date=August 30, 2006 |
| author=Staff | date=August 30, 2006 |
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| url=http://chandra.harvard.edu/photo/2003/bhspin/more.html |
| url=http://chandra.harvard.edu/photo/2003/bhspin/more.html |
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| publisher=Harvard-Smithsonian Center for Astrophysics/Chandra X-ray Center |
| publisher=Harvard-Smithsonian Center for Astrophysics/Chandra X-ray Center |
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| accessdate=2008-03-30 }}</ref>]] |
| accessdate=2008-03-30 }}</ref>]] |
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Objects orbiting black holes probe the gravitational field around the central object. |
Objects orbiting black holes probe the gravitational field around the central object. An early example, discovered in the 1970s, is the accretion disk orbiting the putative black hole responsible for [[Cygnus X-1]], a famous X-ray source. While the material itself cannot be seen directly, the X rays flicker on a millisecond time scale, as expected for hot clumpy material orbiting a ~10 solar-mass black hole just prior to accretion. The X-ray spectrum exhibits the characteristic shape expected for a disk of orbiting relativistic material, with an iron line, emitted at ~6.4 keV, broadened to the red (on the receding side of the disk) and to the blue (on the approaching side). |
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Another example is the [[S2 (star)|star S2]], seen orbiting the [[Galactic center]]. |
Another example is the [[S2 (star)|star S2]], seen orbiting the [[Galactic center]]. Here the star is several light hours from the ~3.5×10<sup>6</sup> solar mass black hole, so its orbital motion can be plotted. Nothing is observed at the center of the observed orbit, the position of the black hole itself—as expected for a black object. |
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===Determining the mass of black holes=== |
===Determining the mass of black holes=== |
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==Black hole candidates== |
==Black hole candidates== |
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===Supermassive black holes at the centers of galaxies=== |
===Supermassive black holes at the centers of galaxies=== |
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[[ |
[[File:M87 jet.jpg|left|thumb|284px|The jet originating from the center of [[Messier 87|M87]] in this image comes from an [[active galactic nucleus]] that may contain a [[supermassive black hole]]. Credit: [[Hubble Space Telescope]]/[[NASA]]/[[ESA]].]] |
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According to the American Astronomical Society, every large galaxy has a supermassive black hole at its center.{{ |
According to the American Astronomical Society, every large galaxy has a supermassive black hole at its center.{{Citation needed|date=October 2008}} The black hole’s mass is proportional to the mass of the host galaxy, suggesting that the two are linked very closely. The [[Hubble Space Telescope]] and ground-based telescopes in Hawaii were used in a large survey of galaxies. |
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For decades, astronomers have used the term "[[active galaxy]]" to describe galaxies with unusual characteristics, such as unusual [[spectral line]] emission and very strong [[radio]] emission.<ref name="krolik1999">{{cite book |
For decades, astronomers have used the term "[[active galaxy]]" to describe galaxies with unusual characteristics, such as unusual [[spectral line]] emission and very strong [[radio]] emission.<ref name="krolik1999">{{cite book |
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| publisher=Princeton University Press |
| publisher=Princeton University Press |
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| location=Princeton, New Jersey |
| location=Princeton, New Jersey |
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| isbn=0-691-01151-6}}{{ |
| isbn=0-691-01151-6}}{{page needed|date=April 2013}}</ref><ref name="sparkegallagher2000">{{cite book |
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| author=L. S. Sparke, J. S. Gallagher III |
| author=L. S. Sparke, J. S. Gallagher III |
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| year=2000 |
| year=2000 |
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| publisher=Cambridge University Press |
| publisher=Cambridge University Press |
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| location=Cambridge |
| location=Cambridge |
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| isbn=0-521-59704-4}}{{ |
| isbn=0-521-59704-4}}{{page needed|date=April 2013}}</ref> However, theoretical and observational studies have shown that the [[Active galactic nucleus|active galactic nuclei]] (AGN) in these galaxies may contain [[supermassive black holes]].<ref name="krolik1999"/><ref name="sparkegallagher2000"/> The models of these AGN consist of a central black hole that may be millions or billions of times more massive than the [[Sun]]; a disk of [[interstellar gas|gas]] and [[interstellar dust|dust]] called an [[Accretion disc|accretion disk]]; and two [[relativistic jet|jets]] that are perpendicular to the accretion disk.<ref name="sparkegallagher2000"/> |
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Although supermassive black holes are expected to be found in most AGN, only some galaxies' nuclei have been more carefully studied in attempts to both identify and measure the actual masses of the central supermassive black hole candidates. Some of the most notable galaxies with supermassive black hole candidates include the [[Andromeda Galaxy]], [[Messier 32|M32]], [[Messier 87|M87]], [[NGC 3115]], [[NGC 3377]], [[NGC 4258]], and the [[Sombrero Galaxy]].<ref name="kormendyrichstone1995">{{cite journal |
Although supermassive black holes are expected to be found in most AGN, only some galaxies' nuclei have been more carefully studied in attempts to both identify and measure the actual masses of the central supermassive black hole candidates. Some of the most notable galaxies with supermassive black hole candidates include the [[Andromeda Galaxy]], [[Messier 32|M32]], [[Messier 87|M87]], [[NGC 3115]], [[NGC 3377]], [[NGC 4258]], and the [[Sombrero Galaxy]].<ref name="kormendyrichstone1995">{{cite journal |
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| author=J. Kormendy, D. Richstone |
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| title=Inward Bound---The Search For Supermassive Black Holes In Galactic Nuclei |
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| journal=Annual Reviews of Astronomy and Astrophysics |
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| year=1995 |
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| volume=33 |
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| pages=581–624 |
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| bibcode=1995ARA&A..33..581K| doi=10.1146/annurev.aa.33.090195.003053}}</ref> |
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| doi=10.1146/annurev.aa.33.090195.003053}}</ref> |
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Astronomers are confident that our own [[Milky Way]] galaxy has a supermassive black hole at its center, in a region called [[Sagittarius A*]]: |
Astronomers are confident that our own [[Milky Way]] galaxy has a supermassive black hole at its center, in a region called [[Sagittarius A*]]: |
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* A star called [[S2 (star)]] follows an [[elliptical]] orbit with a [[orbital period|period]] of 15.2 years and a [[pericenter]] (closest) distance of 17 [[light hour]]s from the central object. |
* A star called [[S2 (star)]] follows an [[elliptical]] orbit with a [[orbital period|period]] of 15.2 years and a [[pericenter]] (closest) distance of 17 [[light hour]]s from the central object. |
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* The first estimates indicated that the central object contains 2.6 million solar masses and has a radius of less than 17 light hours. Only a black hole can contain such a vast mass in such a small volume. |
* The first estimates indicated that the central object contains 2.6 million solar masses and has a radius of less than 17 light hours. Only a black hole can contain such a vast mass in such a small volume. |
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* Further observations<ref>{{cite journal |
* Further observations<ref>{{cite journal |authorlink=Andrea Ghez |title=Stellar Orbits around the Galactic Center Black Hole |journal=The Astrophysical Journal |volume=620 |issue=2 |pages=744–757 |year=2005 |date=May 2005 |url=http://www.journals.uchicago.edu/doi/abs/10.1086/427175 |accessdate=2008-05-10 |doi=10.1086/427175 |arxiv=astro-ph/0306130|last1=Ghez |first1=A. M. |last2=Salim |first2=S. |last3=Hornstein |first3=S. D. |last4=Tanner |first4=A. |last5=Lu |first5=J. R. |last6=Morris |first6=M. |last7=Becklin |first7=E. E. |last8=Duchene |first8=G. |s2cid=8656531 }}</ref> strengthened the case for a black hole, by showing that the central object's mass is about 3.7 million solar masses and its radius no more than 6.25 light-hours. |
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===Intermediate-mass black holes in globular clusters=== |
===Intermediate-mass black holes in globular clusters=== |
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In 2002, the Hubble Space Telescope produced observations indicating that [[globular clusters]] named [[Messier 15|M15]] and [[Mayall II|G1]] may contain [[intermediate-mass black hole]]s.<ref>{{cite arXiv |eprint=astro-ph/ |
In 2002, the Hubble Space Telescope produced observations indicating that [[globular clusters]] named [[Messier 15|M15]] and [[Mayall II|G1]] may contain [[intermediate-mass black hole]]s.<ref>{{cite arXiv |eprint=astro-ph/0209315 |author1=Joris Gerssen |last2=van der Marel | first2=Roeland P. |author3=Karl Gebhardt |author4=Puragra Guhathakurta |author5=Ruth Peterson |author6=Carlton Pryor |title=Hubble Space Telescope Evidence for an Intermediate-Mass Black Hole in the Globular Cluster M15: II. Kinematical Analysis and Dynamical Modeling |class=astro-ph |year=2002}}</ref><ref>{{cite press release |title=Hubble Discovers Black Holes in Unexpected Places |url=http://hubblesite.org/newscenter/archive/releases/cosmology/2002/18/text/ |publisher=[[Space Telescope Science Institute]] |date=2002-09-17 |accessdate=2009-03-14}}</ref> This interpretation is based on the sizes and periods of the orbits of the stars in the globular clusters. But the Hubble evidence is not conclusive, since a group of [[neutron star]]s could cause similar observations. Until recent discoveries, many astronomers thought that the complex gravitational interactions in globular clusters would eject newly-formed black holes. |
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In November 2004 a team of astronomers reported the discovery of the first well-confirmed [[intermediate-mass black hole]] in our Galaxy, orbiting three light-years from Sagittarius A*. This black hole of 1,300 solar masses is within a cluster of seven stars, possibly the remnant of a massive star cluster that has been stripped down by the Galactic Centre.<ref name = "Nature.com-20060325">{{cite |
In November 2004 a team of astronomers reported the discovery of the first well-confirmed [[intermediate-mass black hole]] in our Galaxy, orbiting three light-years from Sagittarius A*. This black hole of 1,300 solar masses is within a cluster of seven stars, possibly the remnant of a massive star cluster that has been stripped down by the Galactic Centre.<ref name = "Nature.com-20060325">{{cite journal |url=http://www.nature.com/news/2004/041108/full/news041108-2.html |title=Second black hole found at the centre of our Galaxy |journal=NatureNews |accessdate=2006-03-25 |doi=10.1038/news041108-2 |year=2004 |last=Peplow |first=Mark|pages=news041108–2 }}</ref><ref name = "edpsciences-usa.org-2004">{{cite arXiv |eprint=astro-ph/0404450 |last1=Maillard | first1=J. P. |last2=Paumard | first2=T. |last3=Stolovy | first3=S. R. |last4=Rigaut | first4=F. |title=The nature of the Galactic Center source IRS 13 revealed by high spatial resolution in the infrared |class=astro-ph |year=2004}}</ref> This observation may add support to the idea that supermassive black holes grow by absorbing nearby smaller black holes and stars. |
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In January 2007, researchers at the University of Southampton in the United Kingdom reported finding a black hole, possibly of about 10 solar masses, in a globular cluster associated with a galaxy named NGC 4472, some 55 million light-years away.<ref>{{cite arXiv |eprint=0805. |
In January 2007, researchers at the University of Southampton in the United Kingdom reported finding a black hole, possibly of about 10 solar masses, in a globular cluster associated with a galaxy named NGC 4472, some 55 million light-years away.<ref>{{cite arXiv |eprint=0805.2952 |last1=Zepf | first1=Stephen E. |author2=Daniel Stern |last3=Maccarone | first3=Thomas J. |author4=Arunav Kundu |author5=Marc Kamionkowski |last6=Rhode | first6=Katherine L. |last7=Salzer | first7=John J. |author8=Robin Ciardullo |author9=Caryl Gronwall |title=Very Broad [O III]4959,5007 Emission from the NGC 4472 Globular Cluster RZ2109 and Implications for the Mass of Its Black Hole X-ray Source |class=astro-ph |year=2008}}</ref><ref>{{cite journal |arxiv=astro-ph/0701310 |last1=Maccarone | first1=Thomas J. |author2=Arunav Kundu |last3=Zepf | first3=Stephen E. |last4=Rhode | first4=Katherine L. |title=A black hole in a globular cluster |journal=Nature |year=2007|volume=445 |issue=7124 |pages=183–185 |doi=10.1038/nature05434 |pmid=17203062 |s2cid=4323113 }}</ref> |
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RZ2109 and Implications for the Mass of Its Black Hole X-ray Source |class=astro-ph |year=2008}}</ref><ref>{{cite arXiv |eprint=astro-ph/0701310v1 |last1=Maccarone | first1=Thomas J. |author2=Arunav Kundu |last3=Zepf | first3=Stephen E. |last4=Rhode | first4=Katherine L. |title=A black hole in a globular cluster |class=astro-ph |year=2007}}</ref> |
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===Stellar-mass black holes in the Milky Way=== |
===Stellar-mass black holes in the Milky Way=== |
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[[ |
[[File:Accretion disk.jpg|right|325px|thumb|Artist's impression of a binary system consisting of a black hole and a [[main sequence]] star. The black hole is drawing matter from the main sequence star via an [[Accretion disc|accretion disk]] around it, and some of this matter forms a [[galactic jet|gas jet]].]] |
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Our Milky Way galaxy contains several probable [[stellar-mass black hole]]s which are closer to us than the supermassive black hole in the [[Sagittarius A*]] region. These candidates are all members of [[X-ray binary]] systems in which the denser object draws matter from its partner via an accretion disk. The probable black holes in these pairs range from three to more than a dozen [[solar mass]]es.<ref name = "Casares-Holes">{{cite arXiv |eprint=astro-ph/ |
Our Milky Way galaxy contains several probable [[stellar-mass black hole]]s which are closer to us than the supermassive black hole in the [[Sagittarius A*]] region. These candidates are all members of [[X-ray binary]] systems in which the denser object draws matter from its partner via an accretion disk. The probable black holes in these pairs range from three to more than a dozen [[solar mass]]es.<ref name = "Casares-Holes">{{cite arXiv |eprint=astro-ph/0612312 |author1=Jorge Casares |title=Observational evidence for stellar-mass black holes |class=astro-ph |year=2006}}</ref><ref name = "Garcia-Jets">{{cite arXiv |eprint=astro-ph/0302230 |last1=Garcia | first1=M. R. |last2=Miller | first2=J. M. |last3=McClintock | first3=J. E. |last4=King | first4=A. R. |last5=Orosz | first5=J. |title=Resolved Jets and Long-Period Black Hole X-ray Novae |class=astro-ph |year=2003}}</ref> The most distant stellar-mass black hole ever observed is a member of a binary system located in the [[Messier 33]] galaxy.<ref>{{cite arXiv |eprint=0710.3165 |last1=Orosz | first1=Jerome A. |last2=McClintock | first2=Jeffrey E. |author3=Ramesh Narayan |last4=Bailyn | first4=Charles D. |last5=Hartman | first5=Joel D. |author6=Lucas Mracri |author7=Jiefeng Liu |author8=Wolfgang Pietsch |last9=Remillard | first9=Ronald A. |author10=Avi Shporer |author11=Tsevi Mazeh |title=A 15.65 solar mass black hole in an eclipsing binary in the nearby spiral galaxy Messier 33 |class=astro-ph |year=2007}}</ref> |
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===Micro black holes=== |
===Micro black holes=== |
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There is theoretically no smallest size for a black hole. Once created, it has the properties of a black hole. [[Stephen Hawking]] theorized that [[primordial black holes]] could evaporate and become even tinier, i.e. [[micro black holes]]. Searches for evaporating primordial black holes are proposed for the [[Fermi Gamma-ray Space Telescope]], which was launched on June 11, 2008. However, if micro black holes can be created by other means, such as by cosmic ray impacts or in colliders, that does not imply that they must evaporate. |
There is theoretically no smallest size for a black hole. Once created, it has the properties of a black hole. [[Stephen Hawking]] theorized that [[primordial black holes]] could evaporate and become even tinier, i.e. [[micro black holes]]. Searches for evaporating primordial black holes are proposed for the [[Fermi Gamma-ray Space Telescope]], which was launched on June 11, 2008. However, if micro black holes can be created by other means, such as by cosmic ray impacts or in colliders, that does not imply that they must evaporate. |
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The formation of black hole analogs on Earth in [[particle accelerators]] has been reported. These black hole analogs are not the same as gravitational black holes, but they are vital testing grounds for quantum theories of gravity.<ref>{{cite arXiv |eprint=hep-th/ |
The formation of black hole analogs on Earth in [[particle accelerators]] has been reported. These black hole analogs are not the same as gravitational black holes, but they are vital testing grounds for quantum theories of gravity.<ref>{{cite arXiv |eprint=hep-th/0501068 |first=Horatiu |last=Nastase |authorlink=Horaţiu Năstase |title=The RHIC fireball as a dual black hole |class=hep-th |year=2005 |author1=Horatiu Nastase}}</ref> |
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They act like black holes because of the [[AdS/CFT correspondence|correspondence]] between the theory of the strong nuclear force, which has nothing to do with gravity, and the quantum theory of gravity. They are similar because both are described by [[string theory]]. So the formation and disintegration of a [[quark-gluon plasma|fireball]] in quark gluon plasma can be interpreted in black hole language. The fireball at the [[Relativistic Heavy Ion Collider]] [RHIC] is a phenomenon which is closely analogous to a black hole, and many of its physical properties can be correctly predicted using this analogy. The fireball, however, is not a gravitational object. It is presently unknown whether the much more energetic [[Large Hadron Collider]] [LHC] would be capable of producing the speculative large extra dimension micro black hole, as many theorists have suggested. See [[Safety of particle collisions at the Large Hadron Collider]] for a more in depth discussion. |
They act like black holes because of the [[AdS/CFT correspondence|correspondence]] between the theory of the strong nuclear force, which has nothing to do with gravity, and the quantum theory of gravity. They are similar because both are described by [[string theory]]. So the formation and disintegration of a [[quark-gluon plasma|fireball]] in quark gluon plasma can be interpreted in black hole language. The fireball at the [[Relativistic Heavy Ion Collider]] [RHIC] is a phenomenon which is closely analogous to a black hole, and many of its physical properties can be correctly predicted using this analogy. The fireball, however, is not a gravitational object. It is presently unknown whether the much more energetic [[Large Hadron Collider]] [LHC] would be capable of producing the speculative large extra dimension micro black hole, as many theorists have suggested. See [[Safety of particle collisions at the Large Hadron Collider]] for a more in depth discussion. |
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==History== |
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==Black holes and Fundamental Physics== |
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The Newtonian conceptions of Michell and Laplace are often referred to as "[[dark star]]s" to distinguish them from the "black holes" of general relativity. |
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===Information loss paradox=== |
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{{Main|Black hole information paradox}} |
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An open question in fundamental physics is the so-called information loss paradox, or [[black hole information paradox|black hole unitarity]] paradox. Classically, the laws of physics are the same run forward or in reverse. That is, if the position and velocity of every particle in the universe were measured, we could (disregarding [[chaos theory|chaos]]) work backwards to discover the history of the universe arbitrarily far in the past. In quantum mechanics, this corresponds to a vital property called [[unitarity]], which has to do with the conservation of probability.<ref name="PlayDice000">{{cite web |
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| title = ''Does God Play Dice?'' Archived Lecture by Professor Steven Hawking, Department of Applied Mathematics and Theoretical Physics (DAMTP) University of Caimbridge |
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| url = http://www.hawking.org.uk/lectures/dice.html |
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| accessdate = 2007-09-07 |
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}}</ref> |
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===Newtonian theories=== |
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Black holes, however, might violate this rule. The position under classical general relativity is subtle but straightforward: because of the classical [[no hair theorem]], we can never determine what went into the black hole. However, as seen from the outside, information is never actually destroyed, as matter falling into the black hole takes an infinite time to reach the event horizon. |
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The concept of a body so massive that even light could not [[Escape velocity|escape]] was put forward by the [[geologist]] [[John Michell]] in a letter written to [[Henry Cavendish]] in 1783 and published by the [[Royal Society]].<ref name = "Michell1784"/> |
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{{cquote|''If the semi-diameter of a sphere of the same density as the Sun were to exceed that of the Sun in the proportion of 500 to 1, a body falling from an infinite height towards it would have acquired at its surface greater velocity than that of light, and consequently supposing light to be attracted by the same force in proportion to its vis inertiae, with other bodies, all light emitted from such a body would be made to return towards it by its own proper gravity.''}} |
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This assumes that light is influenced by gravity in the same way as massive objects. |
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[[Bekenstein bound|Ideas about quantum gravity]], on the other hand, suggest that there can only be a limited finite entropy (i.e. a maximum finite amount of information) associated with the space near the horizon; but the change in the entropy of the horizon plus the entropy of the Hawking radiation is always sufficient to take up all of the entropy of matter and energy falling into the black hole. |
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In 1796, the mathematician [[Pierre-Simon Laplace]] promoted the same idea in the first and second editions of his book ''Exposition du système du Monde'' (it was removed from later editions). |
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Many physicists are concerned however that this is still not sufficiently well understood. In particular, at a quantum level, is the quantum state of the Hawking radiation uniquely determined by the history of what has fallen into the black hole; and is the history of what has fallen into the black hole uniquely determined by the quantum state of the black hole and the radiation? This is what determinism, and unitarity, would require. |
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The idea of black holes was largely ignored in the nineteenth century, since light was then thought to be a massless wave and therefore not influenced by gravity. Unlike a modern black hole, the object behind the horizon is assumed to be stable against collapse. |
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For a long time [[Stephen Hawking]] had opposed such ideas, holding to his original 1975 position that the Hawking radiation is entirely thermal and therefore entirely random, containing none of the information held in material the hole has swallowed in the past; this information he reasoned had been lost. However, on 21 July 2004 he presented a new argument, reversing his previous position.<ref name = "Nature-20040407">{{cite web| url=http://www.nature.com/news/2004/040712/full/040712-12.html| title=Hawking changes his mind about black holes| [email protected]| accessdate=2006-03-25}}</ref> On this new calculation, the entropy (and hence information) associated with the black hole escapes in the Hawking radiation itself. However, making sense of it, even in principle, is difficult until the black hole completes its evaporation. Until then it is impossible to relate in a 1:1 way the information in the Hawking radiation (embodied in its detailed internal correlations) to the initial state of the system. Once the black hole evaporates completely, such identification can be made, and unitarity is preserved. |
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===Theories based on general relativity=== |
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By the time Hawking completed his calculation, it was already very clear from the AdS/CFT correspondence that black holes decay in a unitary way. This is because the fireballs in gauge theories, which are analogous to Hawking radiation, are unquestionably unitary. Hawking's new calculation has not been evaluated by the specialist scientific community, because the methods he uses are unfamiliar and of dubious consistency; but Hawking himself found it sufficiently convincing to pay out on a [[Thorne-Hawking-Preskill bet|bet]] he had made in 1997 with Caltech physicist [[John Preskill]], to considerable media interest. |
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In 1915, Albert Einstein developed the theory of gravity called general relativity, having earlier shown that gravity does influence light (although light has zero [[rest mass]], it is not the rest mass that is the source of gravity but the energy). A few months later, [[Karl Schwarzschild]] gave the [[Schwarzschild metric|solution]] for the gravitational field of a point mass and a spherical mass,<ref name ="Schwarzschild1916"/> showing that a black hole could theoretically exist. The [[Schwarzschild radius]] is now known to be the radius of the [[event horizon]] of a non-rotating black hole, but this was not well understood at that time, for example Schwarzschild himself thought it was not physical. Johannes Droste, a student of [[Hendrik Lorentz|Lorentz]], independently gave the same solution for the point mass a few months after Schwarzschild and wrote more extensively about its properties. |
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In 1930, the [[astrophysicist]] [[Subrahmanyan Chandrasekhar]] argued that, according to [[special relativity]], a non-rotating body above 1.44 solar masses (the [[Chandrasekhar limit]]), would collapse since there was nothing known at that time could stop it from doing so. His arguments were opposed by [[Arthur Eddington]], who believed that something would inevitably stop the collapse. Eddington was partly right: a [[white dwarf]] slightly more massive than the Chandrasekhar limit will collapse into a [[neutron star]]. But in 1939, [[Robert Oppenheimer]] published papers (with various co-authors) which predicted that stars above about three solar masses (the [[Tolman-Oppenheimer-Volkoff limit]]) would collapse into black holes for the reasons presented by Chandrasekhar.<ref>{{cite journal |doi=10.1103/PhysRev.55.374 |title=On Massive Neutron Cores |year=1939 |authorlink=J. Robert Oppenheimer |journal=[[Physical Review]] |volume=55 |issue=4 |pages=374–381 |bibcode=1939PhRv...55..374O|last1=Oppenheimer |first1=J. R. |last2=Volkoff |first2=G. M. }}</ref> |
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===Worm Holes=== |
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{{main|Wormholes}} |
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Oppenheimer and his co-authors used [[Schwarzschild metric|Schwarzschild's system of coordinates]] (the only coordinates available in 1939), which produced [[mathematical singularity|mathematical singularities]] at the [[Schwarzschild radius]], in other words the equations broke down at the Schwarzschild radius because some of the terms were [[infinity|infinite]]. This was interpreted as indicating that the Schwarzschild radius was the boundary of a "bubble" in which time "stopped". For a few years the collapsed stars were known as "frozen stars" because the calculations indicated that an outside observer would see the surface of the star frozen in time at the instant where its collapse takes it inside the Schwarzschild radius. But many physicists could not accept the idea of time standing still inside the Schwarzschild radius, and there was little interest in the subject for over 20 years. |
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[[Image:LorentzianWormhole.jpg|thumb|200px|right|Diagram of a Schwarzschild wormhole.]] |
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General relativity describes the possibility of configurations in which two black holes are connected to each other. Such a configuration is usually called a [[wormhole]]. Wormholes have inspired [[science fiction]] authors because they offer a means to travel quickly over long distances and even time travel. In practice, such configurations, seem completely unfeasible in astrophysics, because no known process seems allow the formation of such objects. |
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In 1958, [[David Finkelstein]] broke the deadlock over "stopped time" and introduced the concept of the [[event horizon]] by presenting the [[Eddington-Finkelstein coordinates]], which enabled him to show that "The Schwarzschild surface ''r'' = 2 ''m'' is not a singularity but acts as a perfect unidirectional membrane: causal influences can cross it but only in one direction".<ref>{{cite journal |doi=10.1103/PhysRev.110.965 |title=Past-Future Asymmetry of the Gravitational Field of a Point Particle |year=1958 |first=David |last=Finkelstein |authorlink=David Finkelstein |journal=[[Physical Review]] |volume=110 |issue=4 |pages=965–967 |url=http://www.physics.gatech.edu/people/faculty/finkelstein/paper1.pdf |bibcode=1958PhRv..110..965F}}</ref> Note that at this stage all theories, including Finkelstein's, covered only non-rotating, uncharged black holes. |
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In 1963, [[Roy Kerr]] extended Finkelstein's analysis by presenting the [[Kerr metric]] (coordinates) and showing how this made it possible to predict the properties of [[rotating black hole]]s.<ref>{{cite journal |doi=10.1103/PhysRevLett.11.237 |title=Gravitational Field of a Spinning Mass as an Example of Algebraically Special Metrics |year=1963 |first=Roy P. |last=Kerr |journal=[[Physical Review Letters]] |volume=11 |issue=5 |pages=237–238}}</ref> In addition to its theoretical interest, Kerr's work made black holes more believable for astronomers, since black holes are formed from stars and all known stars rotate. |
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In 1967, astronomers discovered [[pulsars]], and within a few years could show that the known pulsars were rapidly rotating [[neutron star]]s. Until that time, neutron stars were also regarded as just theoretical curiosities. So the discovery of pulsars awakened interest in all types of ultra-dense objects that might be formed by gravitational collapse. |
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In 1970, [[Stephen Hawking]] and [[Roger Penrose]] proved that black holes are a feature of all solutions to Einstein's equations of gravity, not just of Schwarzschild's, and therefore black holes cannot be avoided in some collapsing objects.<ref name=HawkingPenrose1970/> |
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In 1971, [[Louise Webster]] and [[Paul Murdin]], at the [[Royal Greenwich Observatory]],<ref>{{cite journal |
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| title=Cygnus X-1—a Spectroscopic Binary with a Heavy Companion? |
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| journal=Nature | year=1972 |
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| volume=235 | issue=2 | pages=37–38 |
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| url=http://www.nature.com/nature/journal/v235/n5332/abs/235037a0.html |
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| accessdate=2008-03-10 | doi=10.1038/235037a0 | last1=Webster | first1=B. Louise | last2=Murdin | first2=Paul | s2cid=4195462 }}</ref> and [[Charles Thomas Bolton]], working independently at the [[University of Toronto]]'s [[David Dunlap Observatory]],<ref>{{cite journal |
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| last=Bolton | first=C. T. | year=1972 |
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| title=Identification of Cygnus X-1 with HDE 226868 |
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| journal=Nature | volume=235 | issue=2 | pages=271–273 |
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| url=http://www.nature.com/nature/journal/v235/n5336/abs/235271b0.html |
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| accessdate=2008-03-10 | doi=10.1038/235271b0 | s2cid=4222070 }}</ref> observed [[HDE 226868]] [[wobble]], as if orbiting around an invisible but massive companion. Further analysis led to the declaration that the companion, [[Cygnus X-1]], was in fact a black hole.<ref>{{cite web |
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| last=Rolston | first=Bruce | date=10 November 1997 |
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| url=http://news.utoronto.ca/bin/bulletin/nov10_97/art4.htm |
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| title=The First Black Hole | publisher=University of Toronto |
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| accessdate=2008-03-11 }} |
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</ref><ref>{{cite journal |
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| last=Shipman | first=H. L. |
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| title=The implausible history of triple star models for Cygnus X-1 Evidence for a black hole |
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| journal=Astrophysical Letters |
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| year=1975 | volume=16 | issue=1 | pages=9–12 |
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| bibcode=1975ApL....16....9S}}</ref> |
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==Alternative models== |
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{{Main|Nonsingular black hole models}} |
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Several alternative models, which behave like a black hole but avoid the singularity, have been proposed. However, most researchers judge these concepts artificial, as they are more complicated but do not give near term observable differences from black holes (see [[Occam's razor]]). The most prominent alternative theory is the [[Gravastar]]. |
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In March 2005, physicist [[George Chapline]] at the [[Lawrence Livermore National Laboratory]] in [[California]] proposed that black holes do not exist, and that objects currently thought to be black holes are actually [[dark-energy star]]s. He draws this conclusion from some quantum mechanical analyses.<ref name="Arxiv.org-DarkEnergyStars"/> Although his proposal currently has little support in the physics community, it was widely reported by the media.<ref name = "Arxiv.org-DarkEnergyStars">{{cite arXiv |eprint=astro-ph/0503200 |last1=Chapline | first1=G. |title=Dark Energy Stars |class=astro-ph |year=2005}}</ref><ref name = "Nature-20050503">{{cite journal |
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| url=http://www.nature.com/news/2005/050331/full/news050328-8.html |
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| title=Black holes 'do not exist' |
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| first=Philip |
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| last=Ball |
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| journal=Nature News |
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| year=2005 |
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| accessdate=2009-03-14 |
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| doi=10.1038/news050328-8}}</ref> A similar theory about the non-existence of black holes was later developed by a group of physicists at [[Case Western Reserve University]] in June 2007.<ref>{{cite journal |doi=10.1103/PhysRevD.76.024005 |title=Observation of incipient black holes and the information loss problem |year=2007 |author=Vachaspati, Tanmay |journal=Physical Review D |volume=76 |issue=2 |pages=024005|arxiv=gr-qc/0609024 |s2cid=119333620 }}</ref><ref>{{cite web |url=http://blog.case.edu/case-news/2007/06/20/blackholes |first=Heidi |last=Cool |title=Black holes don't exist, Case physicists report |publisher=[[Case Western Reserve University]] |date=2007-06-20 |accessdate=2009-03-14}}</ref> |
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Among the alternate models are [[magnetospheric eternally collapsing objects]],<ref name=quasar1>{{cite journal |arxiv=astro-ph/0505518 |doi=10.1086/504898 |title=Observations Supporting the Existence of an Intrinsic Magnetic Moment inside the Central Compact Object within the Quasar Q0957+561 |year=2006 |last=Schild |first=Rudolph E. |authorlink=Rudolph Schild |journal=The Astronomical Journal |volume=132 |pages=420–432|s2cid=119355221 }}</ref><ref>{{cite journal |doi=10.1088/0004-6256/135/3/947 |title=Direct Microlensing-Reverberation Observations of the Intrinsic Magnetic Structure of Active Galactic Nuclei in Different Spectral States: A Tale of Two Quasars |year=2008 |last=Schild |first=Rudolph E. |authorlink=Rudolph Schild |journal=The Astronomical Journal |volume=135 |issue=3 |pages=947–956|arxiv=0708.2422 |s2cid=13077229 }}</ref><ref>{{cite arXiv |eprint=0806.1748 |last1=Schild | first1=Rudolph E. |last2=Leiter | first2=Darryl J. |title=Black Hole or MECO? Decided by a Thin Luminous Ring Structure Deep Within Quasar Q0957 |class=astro-ph |year=2008}}</ref> clusters of [[elementary particle]]s<ref name="Maoz 1998"> |
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{{cite journal| url=http://www.iop.org/EJ/article/1538-4357/494/2/L181/975794.web.pdf |
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| journal=The Astrophysical Journal Letters |
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| volume=494 | issue=2 | pages=L181–L184 |
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| year=1998| date=20 February 1998 |
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| title=Dynamical Constraints On Alternatives To Supermassive Black Holes In Galactic Nuclei |
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| first=Eyal| last=Maoz |
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| doi=10.1086/311194 |
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| arxiv=astro-ph/9710309 |
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| bibcode=1998ApJ...494L.181M| s2cid=14218476 |
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}} |
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</ref> (e.g., [[boson star]]s<ref name = "arxiv.org-Torres2000">{{cite journal |arxiv=astro-ph/0004064 |doi=10.1103/PhysRevD.62.104012 |title=Supermassive boson star at the galactic center? |year=2000 |author=Torres, Diego F. |journal=Physical Review D |volume=62 |issue=10 |pages=104012|s2cid=16670960 }}</ref>), [[fermion ball]]s,<ref name = "arxiv.org-Munyanezr2001">{{cite journal |arxiv=astro-ph/0103466 |doi=10.1086/323949 |title=The Motion of Stars near the Galactic Center: A Comparison of the Black Hole and Fermion Ball Scenarios |year=2002 |author=Munyaneza, Faustin |journal=The Astrophysical Journal |volume=564 |pages=274–283|s2cid=119472619 }}</ref> self-gravitating, degenerate heavy [[neutrino]]s<ref name = "arxiv.org-Tsiklauri1998">{{cite journal |arxiv=astro-ph/9805273 |doi=10.1086/305753 |title=Dark Matter Concentration in the Galactic Center |year=1998 |author=Tsiklauri, David |journal=The Astrophysical Journal |volume=500 |issue=2 |pages=591–595|s2cid=8988824 }}</ref> and even clusters of very low mass (~0.04 solar mass) black holes.<ref name="Maoz 1998"/> |
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==More advanced topics== |
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===Holographic world=== |
===Holographic world=== |
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===Entropy and Hawking radiation=== |
===Entropy and Hawking radiation=== |
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In 1971, [[Stephen Hawking]] showed that the total area of the event horizons of any collection of classical black holes can never decrease, even if they collide and swallow each other; that is merge.<ref>{{cite book |first=Stephen |last=Hawking |authorlink=Stephen Hawking |title=[[A Brief History of Time]] |publisher=Bantam Books |location=New York |year=1998 |pages= |isbn=0-553-38016-8}}{{ |
In 1971, [[Stephen Hawking]] showed that the total area of the event horizons of any collection of classical black holes can never decrease, even if they collide and swallow each other; that is merge.<ref>{{cite book |first=Stephen |last=Hawking |authorlink=Stephen Hawking |title=[[A Brief History of Time]] |publisher=Bantam Books |location=New York |year=1998 |pages= |isbn=0-553-38016-8}}{{page needed|date=April 2013}}</ref> This is remarkably similar to the Second Law of [[Thermodynamics]], with area playing the role of [[entropy]]. As a classical object with zero temperature it was assumed that black holes had zero entropy; if so the second law of thermodynamics would be violated by an entropy-laden material entering the black hole, resulting in a decrease of the total entropy of the universe. Therefore, [[Jacob Bekenstein]] proposed that a black hole should have an entropy, and that it should be proportional to its horizon area. Since black holes do not classically emit radiation, the thermodynamic viewpoint seemed simply an analogy, since zero temperature implies infinite changes in entropy with any addition of heat, which implies infinite entropy. However, in 1974, Hawking applied [[quantum field theory]] to the curved spacetime around the event horizon and discovered that black holes emit [[Hawking radiation]], a form of [[thermal radiation]], allied to the [[Unruh effect]], which implied they had a positive temperature. This strengthened the analogy being drawn between black hole dynamics and thermodynamics: using the [[Laws of black hole mechanics#The First Law|first law of black hole mechanics]], it follows that the entropy of a non-rotating black hole is one quarter of the area of the horizon. This is a universal result and can be extended to apply to cosmological horizons such as in [[de Sitter space]]. It was later suggested that black holes are maximum-entropy objects, meaning that the maximum possible entropy of a region of space is the entropy of the largest black hole that can fit into it. This led to the [[holographic principle]]. |
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The Hawking radiation reflects a characteristic [[temperature]] of the black hole, which can be calculated from its entropy. The more its temperature falls, the more massive a black hole becomes: the more energy a black hole absorbs, the colder it gets. A black hole with roughly the [[Orders of magnitude (mass)#23|mass of the planet Mercury]] would have a temperature in equilibrium with the cosmic microwave background radiation (about 2.73 K). More massive than this, a black hole will be colder than the background radiation, and it will gain energy from the background faster than it gives energy up through Hawking radiation, becoming even colder still. However, for a less massive black hole the effect implies that the mass of the black hole will slowly evaporate with time, with the black hole becoming hotter and hotter as it does so. Although these effects are negligible for black holes massive enough to have been formed astronomically, they would rapidly become significant for hypothetical [[micro black hole|smaller black holes]], where quantum-mechanical effects dominate. Indeed, small black holes are predicted to undergo runaway evaporation and eventually vanish in a burst of radiation. |
The Hawking radiation reflects a characteristic [[temperature]] of the black hole, which can be calculated from its entropy. The more its temperature falls, the more massive a black hole becomes: the more energy a black hole absorbs, the colder it gets. A black hole with roughly the [[Orders of magnitude (mass)#23|mass of the planet Mercury]] would have a temperature in equilibrium with the cosmic microwave background radiation (about 2.73 K). More massive than this, a black hole will be colder than the background radiation, and it will gain energy from the background faster than it gives energy up through Hawking radiation, becoming even colder still. However, for a less massive black hole the effect implies that the mass of the black hole will slowly evaporate with time, with the black hole becoming hotter and hotter as it does so. Although these effects are negligible for black holes massive enough to have been formed astronomically, they would rapidly become significant for hypothetical [[micro black hole|smaller black holes]], where quantum-mechanical effects dominate. Indeed, small black holes are predicted to undergo runaway evaporation and eventually vanish in a burst of radiation. |
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[[Image:First Gold Beam-Beam Collision Events at RHIC at 100 100 GeV c per beam recorded by STAR.jpg|thumb|left|400px|If ultra-high-energy collisions of particles in a [[particle accelerator]] can create microscopic black holes, it is expected that all types of particles will be emitted by black hole evaporation, providing key evidence for any [[grand unified theory]]. Above are the high energy particles produced in a gold ion collision on the [[Relativistic Heavy Ion Collider|RHIC]].]] |
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Although general relativity can be used to perform a semi-classical calculation of black hole entropy, this situation is theoretically unsatisfying. In [[statistical mechanics]], entropy is understood as counting the number of microscopic configurations of a system which have the same macroscopic qualities(such as [[mass]], [[Charge (physics)|charge]], [[pressure]], etc.). But without a satisfactory theory of [[quantum gravity]], one cannot perform such a computation for black holes. Some promise has been shown by [[string theory]], however. There one posits that the microscopic degrees of freedom of the black hole are [[D-brane]]s. By counting the states of D-branes with given charges and energy, the entropy for certain [[supersymmetric]] black holes has been reproduced. Extending the region of validity of these calculations is an ongoing area of research. |
Although general relativity can be used to perform a semi-classical calculation of black hole entropy, this situation is theoretically unsatisfying. In [[statistical mechanics]], entropy is understood as counting the number of microscopic configurations of a system which have the same macroscopic qualities(such as [[mass]], [[Charge (physics)|charge]], [[pressure]], etc.). But without a satisfactory theory of [[quantum gravity]], one cannot perform such a computation for black holes. Some promise has been shown by [[string theory]], however. There one posits that the microscopic degrees of freedom of the black hole are [[D-brane]]s. By counting the states of D-branes with given charges and energy, the entropy for certain [[supersymmetric]] black holes has been reproduced. Extending the region of validity of these calculations is an ongoing area of research. |
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Many physicists are concerned however that this is still not sufficiently well understood. In particular, at a quantum level, is the quantum state of the Hawking radiation uniquely determined by the history of what has fallen into the black hole; and is the history of what has fallen into the black hole uniquely determined by the quantum state of the black hole and the radiation? This is what determinism, and unitarity, would require. |
Many physicists are concerned however that this is still not sufficiently well understood. In particular, at a quantum level, is the quantum state of the Hawking radiation uniquely determined by the history of what has fallen into the black hole; and is the history of what has fallen into the black hole uniquely determined by the quantum state of the black hole and the radiation? This is what determinism, and unitarity, would require. |
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For a long time [[Stephen Hawking]] had opposed such ideas, holding to his original 1975 position that the Hawking radiation is entirely thermal and therefore entirely random, containing none of the information held in material the hole has swallowed in the past; this information he reasoned had been lost. However, on 21 July 2004 he presented a new argument, reversing his previous position.<ref name = "Nature-20040407">{{cite |
For a long time [[Stephen Hawking]] had opposed such ideas, holding to his original 1975 position that the Hawking radiation is entirely thermal and therefore entirely random, containing none of the information held in material the hole has swallowed in the past; this information he reasoned had been lost. However, on 21 July 2004 he presented a new argument, reversing his previous position.<ref name = "Nature-20040407">{{cite journal |url=http://www.nature.com/news/2004/040715/full/news040712-12.html |title=Hawking changes his mind about black holes |journal=Nature News |year=2004 |accessdate=2006-03-25 |doi=10.1038/news040712-12|last1=Peplow |first1=Mark }}</ref> On this new calculation, the entropy (and hence information) associated with the black hole escapes in the Hawking radiation itself. However, making sense of it, even in principle, is difficult until the black hole completes its evaporation. Until then it is impossible to relate in a 1:1 way the information in the Hawking radiation (embodied in its detailed internal correlations) to the initial state of the system. Once the black hole evaporates completely, such identification can be made, and unitarity is preserved. |
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By the time Hawking completed his calculation, it was already very clear from the AdS/CFT correspondence that black holes decay in a unitary way. This is because the fireballs in gauge theories, which are analogous to Hawking radiation, are unquestionably unitary. Hawking's new calculation has not been evaluated by the specialist scientific community, because the methods he uses are unfamiliar and of dubious consistency; but Hawking himself found it sufficiently convincing to pay out on a [[Thorne-Hawking-Preskill bet|bet]] he had made in 1997 with Caltech physicist [[John Preskill]], to considerable media interest. |
By the time Hawking completed his calculation, it was already very clear from the AdS/CFT correspondence that black holes decay in a unitary way. This is because the fireballs in gauge theories, which are analogous to Hawking radiation, are unquestionably unitary. Hawking's new calculation has not been evaluated by the specialist scientific community, because the methods he uses are unfamiliar and of dubious consistency; but Hawking himself found it sufficiently convincing to pay out on a [[Thorne-Hawking-Preskill bet|bet]] he had made in 1997 with Caltech physicist [[John Preskill]], to considerable media interest. |
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<!--==Mathematical theory of non-rotating, uncharged black holes== |
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{{see|Schwarzschild metric |Deriving the Schwarzschild solution}} |
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===Black holes in 3 dimensions=== |
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A black hole solution is also known for 3 dimensional spacetimes. This so called [[BTZ black hole]] exists however only for a negative cosmological constant. |
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In general relativity, there are many known solutions of the [[Einstein field equations]] which describes [[Black hole#Types of black holes|different types of black holes]]. The [[Schwarzschild metric]] is one of the earliest and simplest solutions. This solution describes the [[curvature]] of [[spacetime]] in the vicinity of a static and [[sphere|spherically]] [[symmetry|symmetric]] uncharged object, where the [[Metric space|metric]] is, |
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:<math> \mathrm{d}s^2 = - c^2 \left( 1 - {2Gm \over c^2 r} \right) \mathrm{d}t^2 + \left( 1 - {2Gm \over c^2 r} \right)^{-1} \mathrm{d}r^2 + r^2 \mathrm{d}\Omega^2 </math>, |
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where <math>\mathrm{d}\Omega^2 = \mathrm{d}\theta^2 + \sin^2\theta\; \mathrm{d}\phi^2</math> is a standard element of solid angle. |
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According to general relativity, a gravitating object will collapse into a black hole if its radius is smaller than a characteristic distance, known as the [[Schwarzschild radius]]. (Indeed, [[Buchdahl's theorem]] in general relativity shows that in the case of a [[fluid solution|perfect fluid model]] of a compact object, the true lower limit is somewhat larger than the Schwarzschild radius.) Below this radius, spacetime is so strongly curved that any light ray emitted in this region, regardless of the direction in which it is emitted, will travel towards the centre of the system. Because [[special relativity|relativity]] forbids anything from traveling [[faster-than-light|faster than light]], anything below the Schwarzschild radius – including the constituent particles of the gravitating object – will collapse into the centre. A [[gravitational singularity]], a region of theoretically infinite density, forms at this point. Because not even light can escape from within the Schwarzschild radius, a classical black hole would truly appear [[black]]. |
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The Schwarzschild radius is given by |
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:<math>r_{\rm S} = {2\,Gm \over c^2} </math> |
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where ''G'' is the [[gravitational constant]], ''m'' is the [[mass]] of the object, and ''c'' is the [[speed of light]]. For an object with the mass of the [[Earth]], the Schwarzschild radius is a mere 9 millimeters—about the size of a [[marble (toy)|marble]]. |
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The mean density inside the Schwarzschild radius decreases as the mass of the black hole increases, so while an earth-mass black hole would have a density of 2 × 10<sup>30</sup> kg/m³, a supermassive black hole of 10<sup>9</sup> [[solar mass]]es has a density of around 20 kg/m³, less than water! The mean density is given by |
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:<math>\rho=\frac{3\,c^6}{32\pi m^2G^3}.</math> |
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Since the Earth has a mean radius of 6371 km, its volume would have to be reduced 4 × 10<sup>26</sup> times to collapse into a black hole. For an object with the mass of the [[Sun]], the Schwarzschild radius is approximately 3 km, much smaller than the Sun's current radius of about 696,000 km. It is also significantly smaller than the radius to which the Sun will ultimately shrink after exhausting its nuclear fuel, which is several thousand kilometers. More massive stars can collapse into black holes at the end of their lifetimes. |
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The formula also implies that any object with a given mean density is a black hole if its radius is large enough. The same formula applies for [[white holes]] as well. For example, if the [[observable universe]] has a mean density equal to the [[critical density]], then it is a [[white hole]], since its [[Gravitational singularity|singularity]] is in the past and not in the future as should be for a black hole. |
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There is also the Black Hole Entropy formula: |
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:<math>S = \frac{Akc^3}{4\hbar G}.</math> |
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Where '''A''' is the area of the event horizon of the black hole, '''<math>\hbar</math>''' is [[Dirac's constant]] (the "reduced [[Planck constant]]"), '''k''' is the [[Boltzmann constant]], '''G''' is the [[gravitational constant]], '''c''' is the [[speed of light]] and '''S''' is the [[entropy]]. |
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A convenient length scale to measure black hole processes is the "gravitational radius", which is equal to |
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:<math>r_{\rm G} = {Gm \over c^2} .</math> |
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When expressed in terms of this length scale, many phenomena appear at integer radii. |
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For example, the radius of a Schwarzschild black hole is two gravitational radii and the radius of a maximally rotating Kerr black hole is one gravitational radius. The location of the light circularization radius around a Schwarzschild black hole (where light may orbit the hole in an unstable circular orbit) is <math>3r_{\rm G}</math>. The location of the marginally stable orbit, thought to be close to the inner edge of an accretion disk, is at <math>6r_{\rm G}</math> for a Schwarzschild black hole. --> |
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==References== |
==References== |
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==Further reading== |
==Further reading== |
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===Popular reading=== |
===Popular reading=== |
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* {{ |
* {{cite book |last=Ferguson |first=Kitty |authorlink=Kitty Ferguson |title=Black Holes in Space-Time |publisher=Watts Franklin |year=1991 |isbn=0-531-12524-6}} |
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* {{ |
* {{cite book |first=Stephen |last=Hawking |authorlink=Stephen Hawking |title=[[A Brief History of Time]] |publisher=[[Bantam Books]] |year=1988 |isbn=0-553-38016-8}} |
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* {{ |
* {{cite book |first=Stephen |last=Hawking |authorlink=Stephen Hawking |coauthors=[[Roger Penrose]] |title=The Nature of Space and Time |year=1996 |publisher=[[Princeton University Press]] |isbn=0-691-03791-2 |url=https://books.google.com/books?id=LstaQTXP65cC}} |
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* {{ |
* {{cite book |first=Fulvio |last=Melia |authorlink=Fulvio Melia | title=The Black Hole at the Center of Our Galaxy |publisher=[[Princeton University Press]] |year=2003 |isbn=978-0-691-09505-9}} |
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* {{ |
* {{cite book |first=Fulvio |last=Melia |authorlink=Fulvio Melia |title=The Edge of Infinity: Supermassive Black Holes in the Universe |url=https://books.google.com/books?id=zdDuF2Wu6WEC |publisher=[[Cambridge University Press]] |year=2003 |isbn=978-0-521-81405-8}} |
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* {{ |
* {{cite book |last=Pickover |first=Clifford |authorlink=Clifford A. Pickover |title=Black Holes: A Traveler's Guide |publisher=[[John Wiley & Sons]] |year=1998 |isbn=0-471-19704-1}} |
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* {{ |
* {{cite book |last=Thorne |first=Kip S. |authorlink=Kip Thorne |title=[[Black Holes and Time Warps]] |publisher=[[W. W. Norton & Company]] |year=1994 |isbn=0-393-31276-3}} |
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* {{ |
* {{cite web |last=Stern |first=Borris |title=Blackhole |url=http://www.wikilivres.info/wiki/Blackhole_%28Stern%29 |
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|year=2008}} |
|year=2008}} |
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===University textbooks and monographs=== |
===University textbooks and monographs=== |
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* {{ |
* {{cite book |last=Carter |first=B. |year=1973 |chapter=Black hole equilibrium states |title=Black Holes |editor-last=DeWitt |editor-first=B.S. |editor1-link=Bryce De Witt |editor2-last=DeWitt |editor2-first=C.}} |
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* {{ |
* {{cite book |last=Chandrasekhar |first=Subrahmanyan |title=Mathematical Theory of Black Holes |publisher=Oxford University Press |year=1999 |isbn=0-19-850370-9}} |
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* {{ |
* {{cite book |last1=Frolov |first1=V.P. |last2=Novikov |first2=I.D. |year=1998 |title=Black hole physics}} |
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* {{ |
* {{cite book |last1=Hawking |first1=S.W. |author-link=Stephen Hawking |last2=Ellis |first2=G.F.R. |title=Large Scale Structure of space time |publisher=Cambridge University Press |year=1973 |url=https://books.google.com/books?id=QagG_KI7Ll8C |isbn=0521099064}} |
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* {{ |
* {{cite book |author=[[Fulvio Melia|Melia, Fulvio]] |title=The Galactic Supermassive Black Hole |publisher=Princeton U Press |year=2007 |isbn=978-0-691-13129-0}} |
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* {{ |
* {{cite book |author1=Taylor, Edwin F. |author2=Wheeler, John Archibald |author2-link=John Wheeler |title=Exploring Black Holes | publisher=Addison Wesley Longman |year=2000 |isbn=0-201-38423-X}} |
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* {{cite book |author1=Thorne, Kip S. |author2=Misner, Charles |author3=Wheeler, John |author1-link=Kip Thorne |author2-link=Charles W. Misner |author3-link=John Wheeler |title=Gravitation |publisher=W. H. Freeman and Company |year=1973 |isbn=0-7167-0344-0}} |
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title=Exploring Black Holes | publisher=Addison Wesley Longman | |
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* {{cite book |last=Wald |first=Robert M. |authorlink=Robert Wald |title=Space, Time, and Gravity: The Theory of the Big Bang and Black Holes |publisher=University of Chicago Press |year=1992 |isbn=0-226-87029-4}} |
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year=2000 | id=ISBN 0-201-38423-X}}. |
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* {{Citation |author1=Thorne, Kip S. |author2=Misner, Charles |author3=Wheeler, John |author1-link=Kip Thorne |author2-link=Charles W. Misner|author3-link=John Wheeler | title=Gravitation | publisher=W. H. Freeman and Company | year=1973 | id=ISBN 0-7167-0344-0}}. |
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* {{Citation | author=Wald, Robert M. |author-link=Robert Wald | title=Space, Time, and Gravity: The Theory of the Big Bang and Black Holes | publisher= University of Chicago Press| year=1992 | id=ISBN 0-226-87029-4}}. |
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===Research papers=== |
===Research papers=== |
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* {{cite journal | |
* {{cite journal |arxiv=hep-th/0507171 |doi=10.1103/PhysRevD.72.084013 |title=Information loss in black holes |year=2005 |author=Hawking, S. |journal=Physical Review D |volume=72 |issue=8 |pages=084013|s2cid=118893360 }} Stephen Hawking's purported solution to the black hole [[unitarity]] paradox, first reported at a conference in July 2004. |
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* {{cite journal | |
* {{cite journal |arxiv=astro-ph/0306130 |doi=10.1086/427175 |title=Stellar Orbits around the Galactic Center Black Hole |year=2005 |author=Ghez, A. M. |journal=The Astrophysical Journal |volume=620 |issue=2 |pages=744–757|s2cid=8656531 }} More accurate mass and position for the black hole at the centre of the Milky Way. |
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* {{cite arXiv |eprint=hep-ph/ |
* {{cite arXiv |eprint=hep-ph/0511217 |last1=Hughes | first1=Scott A. |title=Trust but verify: The case for astrophysical black holes |class=hep-ph |year=2005}} Lecture notes from 2005 [[SLAC]] Summer Institute. |
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==External links== |
==External links== |
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* |
*{{cite news |url=http://news.bbc.co.uk/2/hi/science/nature/7774287.stm |title=Black Hole confirmed in Milky Way |first=Pallab |last=Ghosh |date=2008-12-09 |publisher=[[BBC News]] |accessdate=2009-03-15}} |
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*[http://video.google.com/videoplay?docid=-6215434494081736769&hl=en Yale University Video Lecture: Introduction to Black Holes] at Google Video |
*[http://video.google.com/videoplay?docid=-6215434494081736769&hl=en Yale University Video Lecture: Introduction to Black Holes] at Google Video |
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* [http://hubblesite.org/explore_astronomy/black_holes/ Black Holes: Gravity's Relentless Pull] - Award-winning interactive multimedia Web site about the physics and astronomy of black holes from the Space Telescope Science Institute |
* [http://hubblesite.org/explore_astronomy/black_holes/ Black Holes: Gravity's Relentless Pull] - Award-winning interactive multimedia Web site about the physics and astronomy of black holes from the Space Telescope Science Institute |
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* [https://blue.utb.edu/newsandinfo/2006%AD%AD_04_13BreakthroughBlackHoles.htm UT Brownsville Group Simulates Spinning Black-Hole Binaries] |
* [https://blue.utb.edu/newsandinfo/2006%AD%AD_04_13BreakthroughBlackHoles.htm UT Brownsville Group Simulates Spinning Black-Hole Binaries] |
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* [http://www.sciencedaily.com/news/space_time/black_holes/ Black Hole Research News] on [http://www.sciencedaily.com/ ScienceDaily] |
* [http://www.sciencedaily.com/news/space_time/black_holes/ Black Hole Research News] on [http://www.sciencedaily.com/ ScienceDaily] |
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* |
*{{cite journal |url=http://www.sciam.com/article.cfm?id=the-galactic-odd-couple |journal=[[Scientific American]] |date=July 2003 |year=2003 |title=The Galactic Odd Couple |first=Kimberly |last=Weaver|volume=289 |issue=1 |pages=34–41 |doi=10.1038/scientificamerican0703-34 |pmid=12840944 }} |
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* |
*{{cite journal |url=http://www.sciam.com/article.cfm?id=quantum-black-holes |journal=[[Scientific American]] |date=May 2005 |title=Quantum Black Holes |volume=292 |issue=5 |pages=48–55 |doi=10.1038/scientificamerican0505-48 |pmid=15882021 |last1=Carr |first1=Bernard J. |last2=Giddings |first2=Steven B. }} |
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* [http://www.space.com/blackholes/ SPACE.com All About Black Holes] - News, Features and Interesting Original Videos |
* [http://www.space.com/blackholes/ SPACE.com All About Black Holes] - News, Features and Interesting Original Videos |
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* [http://www.damtp.cam.ac.uk/user/gr/public/bh_intro.html Black Holes Intro] - Introduction to Black Holes |
* [http://www.damtp.cam.ac.uk/user/gr/public/bh_intro.html Black Holes Intro] - Introduction to Black Holes |
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* [http://thefutureofthings.com/news/1313/is-the-mass-of-black-holes-limited.html Is the Mass of Black Holes Limited?] - [[The Future of Things]] article |
* [http://thefutureofthings.com/news/1313/is-the-mass-of-black-holes-limited.html Is the Mass of Black Holes Limited?] - [[The Future of Things]] article |
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Revision as of 09:29, 22 June 2024
{{Multiple issues| article = y | long = March 2008 | refimprove = October 2008 | restructure = October 2008 <!-- Too many short sections, per Wikipedia:Layout; non-unique section names, per WP:HEAD --> | jargon = October 2008 }}
![](http://upload.wikimedia.org/wikipedia/commons/thumb/c/cd/Black_Hole_Milkyway.jpg/200px-Black_Hole_Milkyway.jpg)
General relativity |
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In general relativity, a black hole is a region of space in which the gravitational field is so powerful that nothing, including electromagnetic radiation (e.g. visible light), can escape its pull after having fallen past its event horizon. The term derives from the fact that absorption of visible light renders the hole's interior invisible, and indistinguishable from the black space around it.
Despite its invisible interior, a black hole may reveal its presence through interaction with matter orbiting the event horizon. For example, a black hole may be perceived by tracking the movement of a group of stars that orbit its center. Alternatively, one may observe gas (from a nearby star, for instance) that has been drawn into the black hole. The gas spirals inward, heating up to very high temperatures and emitting large amounts of radiation that can be detected from earthbound and earth-orbiting telescopes.[2][3] Such observations have resulted in the general scientific consensus that—barring a breakdown in our understanding of nature—black holes do exist in our universe.[4]
The idea of an object with gravity strong enough to prevent light from escaping was proposed in 1783 by John Michell,[5] an amateur British astronomer. In 1795, Pierre-Simon Laplace, a French physicist independently came to the same conclusion.[6][7] However, such "Newtonian black holes" are very different from black holes in general relativity. They prevent only light from escaping (not, for example, a rocket ship) and only in certain Newtonian models of light (such as an emission theory).
Black holes, as currently understood, are described by the general theory of relativity. This theory predicts that when a large enough amount of mass is present in a sufficiently small region of space, all paths through space are warped inwards towards the center of the volume, preventing all matter and radiation within it from escaping.
While general relativity describes a black hole as a region of empty space with a point-like singularity at the center and an event horizon at the outer edge, the description changes when the effects of quantum mechanics are taken into account. Research indicates that, rather than holding captured matter forever, black holes slowly leak a form of thermal energy called Hawking radiation and have a finite lifetime.[8][9][10] The as yet unknown theory of quantum gravity is believed to give the fully correct description of black holes.
Etymology
The term black hole to describe this phenomenon dates from the mid-1960s, though its precise origins are unclear. Physicist John Wheeler is widely credited with coining it in his 1967 public lecture Our Universe: the Known and Unknown, as an alternative to the more cumbersome "gravitationally completely collapsed star". However, Wheeler insisted that someone else at the conference had coined the term and he had merely adopted it as useful shorthand. The term was also cited in a 1964 letter by Anne Ewing to the AAAS:[11]
“ | According to Einstein’s general theory of relativity, as mass is added to a degenerate star a sudden collapse will take place and the intense gravitational field of the star will close in on itself. Such a star then forms a "black hole" in the universe. | ” |
The phrase had already entered the language years earlier as the Black Hole of Calcutta incident of 1756 in which 146 Europeans were locked up overnight in punishment cell of barracks at Fort William by Siraj ud-Daulah, and all but 23 perished.[12]
The phenomenon appeared in science fiction in a radio episode of Space Patrol which aired October 25, 1952, in which it was called a "cycloplex" or a "hole in space".[citation needed]
What makes it impossible to escape from black holes?
![]() Far away from the black hole a particle can move in any direction. It is only restricted by the speed of light. |
![]() Closer to the black hole spacetime starts to deform. There are more paths going towards the black hole than paths moving away. |
![]() Inside of the event horizon all paths bring the particle closer to the center of the black hole. It is no longer possible for the particle to escape. The diagrams here are effectively Finkelstein diagrams using an advanced time parameter.[13] |
Popular accounts commonly try to explain the black hole phenomenon by using the concept of escape velocity,[14][15] the speed needed for a vessel starting at the surface of a massive object to completely clear the object's gravitational field. It follows from Newton's law of gravity that a sufficiently dense object's escape velocity will equal or even exceed the speed of light. Citing that nothing can exceed the speed of light they then infer that nothing would be able to escape such a dense object.[16] However, the argument can only be seen as an incomplete analogy. It explains neither why light should be affected by gravity in the first place, why it cannot travel beyond the horizon, nor why a rocket-powered spaceship would not be able to break free.
Two concepts introduced by Albert Einstein are needed to explain the phenomenon. The first is that time and space are not two independent concepts, but are interrelated forming a single continuum, spacetime. This continuum has some special properties. An object is not free to move around spacetime at will; it must always move forward in time and cannot change its position in space faster than the speed of light.[17] This is the main result of the theory of special relativity.
The second concept is the base of general relativity; mass deforms the structure of this spacetime.[18] The effect of a mass on spacetime can informally be described as tilting the direction of time towards the mass. As a result, objects tend to move towards masses. This is experienced as gravity. This tilting effect becomes more pronounced as the distance to the mass becomes smaller.[19] At some point close to the mass, the tilting becomes so strong that all the possible paths an object can take lead towards the mass.[20] This implies that any object that crosses this point can no longer get further away from the mass, not even using powered flight. This point is called the event horizon.
Properties: mass, charge, and angular momentum
The No hair theorem states that in a steady state, a black hole has only three independent physical properties: mass, charge and angular momentum.[21] Any two black holes that share the same values for these properties are indistinguishable. When a black hole swallows matter, its horizon oscillates like a membrane with internal friction, a dissipative system. This contrasts with other fundamental physical objects, which behave in a way that is time reversible.
Because a black hole only has a few parameters, a great deal of information is lost when a star collapses to form a black hole. The black hole irreversibly settles down to a simple final state. In classical theories described by a Hamiltonian, Liouville's theorem guarantees that information is always preserved, so that the initial state can be reconstructed from the final state, in principle. Liouville's theorem fails for dissipative systems, like a viscous fluid. In that case the fluid eventually stops, irreversibly hiding information about the initial conditions. In a fluid, the lost information is presumably encoded in a complicated way in the motion of the atoms. For a black hole, it is hard to see where the information is hiding.
The loss of information in black holes is puzzling, because General Relativity is a Lagrangian theory, which superficially appears to be time reversible and Hamiltonian. But because of the horizon, a black hole is not time reversible – it swallows matter but it never spits it out. This irreversible character is an even more serious problem in quantum mechanics, because a quantum theory can only be properly formulated when a system is non-dissipative. Physicists call the conflict between quantum mechanics and black hole dynamics the black hole information paradox.
The No Hair theorem makes some assumptions about the nature of our universe and the matter it contains, and other assumptions lead to different conclusions. For example, if nature allows magnetic monopoles, which is theoretically possible but they have never been observed, then black holes could also have magnetic charge. If there are long range gauge forces other than electromagnetism, then black holes could be charged under those fields as well.
A charged black hole repels other like charges just like any other charged object, despite the fact that photons, the particles responsible for electric and magnetic forces, can't escape. The reason is that electric charge is always visible far away, by Gauss's law, so that no matter what happens inside a big sphere, so long as no charged particles go in or out, the total electric flux stays the same. When charge falls into a black hole, electric field lines remain, and these field lines remember the total charge of all the infalling matter. The electric field lines eventually spread out evenly over the surface of the black hole, settling down to a uniform field-line density on the surface. The black hole acts in this regard like a classical conducting sphere with a definite resistivity.[22]
Black holes in more than four dimensions, or in Anti de Sitter space, can have all sorts of "hair". This is important for extensions of General Relativity like string theory or Kaluza Klein theory, but in our apparently four-dimensional, very nearly flat universe, the no-hair theorem should hold.[23]
Black hole types
The simplest black hole is one that has mass but neither charge nor angular momentum. These black holes are often referred to as Schwarzschild black holes after the physicist Karl Schwarzschild who discovered this solution in 1915.[24] It was the first non-trivial exact solution to the Einstein equations to be discovered, and according to Birkhoff's theorem, the only vacuum solution that is spherically symmetric. For real world physics this means that there is no observable difference between the gravitational field of such a black hole and that of any other spherical object of the same mass—for example a spherical star or planet—once one is in the empty space outside the object. The popular notion of a black hole "sucking in everything" in its surroundings is therefore incorrect; the external gravitational field, far from the event horizon, is essentially like that of ordinary massive bodies.
More general black hole solutions were discovered later in the 20th century. The Reissner-Nordström solution describes a black hole with electric charge, while the Kerr solution yields a rotating black hole. The most general known stationary black hole solution is the Kerr-Newman metric, having both charge and angular momentum. All these general solutions share the property that they converge to the Schwarzschild solution at distances that are large compared to the ratio of charge and angular momentum to mass (in natural units).
While the mass of a black hole can take any (positive) value, the other two properties, charge and angular momentum, are constrained by the mass. In natural units, the total charge Q and the total angular momentum J are expected to satisfy Q2+(J/M)2 ≤ M2 for a black hole of mass M. Black holes saturating this inequality are called extremal. Solutions of Einstein's equations violating the inequality do exist, but do not have a horizon. These solutions have naked singularities and are deemed unphysical, as the cosmic censorship hypothesis states that it is impossible for such singularities to form due to the generic gravitational collapse of realistic matter.[25] This is supported by numerical simulations.[26]
Black holes forming from the collapse of stars are expected—due to the relatively large strength of electromagnetic force—to retain the nearly neutral charge of the star. Rotation, however, is expected to be a common feature of compact objects, and the black-hole candidate binary X-ray source GRS 1915+105[27] appears to have an angular momentum near the maximum allowed value.
Sizes
Class | Mass | Size |
---|---|---|
Supermassive black hole | ~105 - 109 MSun | ~0.001–10 AU |
Intermediate-mass black hole | ~103 MSun | ~103 km = REarth |
Stellar-mass black holes | ~10 MSun | ~30 km |
Primordial black hole | up to ~MMoon | up to ~0.1 mm |
Black holes occurring in nature are commonly classified according to their mass, independent of angular momentum J. The size of a black hole, as determined by the radius of the event horizon, or Schwarzschild radius, is proportional to the mass through where is the Schwarzschild radius and is the mass of the Sun. Thus, size and mass have a simple relationship, which is independent of rotation. The size (volume) of a black hole is defined by its event horizon, as its true potential volume within the event horizon is indistinguishable. Some physicists contend that black holes are infinitesimally small. According to this mass/size criterion then, black holes are commonly classified as:
- Supermassive black holes that contain hundreds of thousands to billions of solar masses are believed to exist in the center of most galaxies, including our own Milky Way. They are thought to be responsible for active galactic nuclei, and presumably form either from the coalescence of smaller black holes, or by the accretion of stars and gas onto them. The largest known supermassive black hole is located in OJ 287 weighing in at 18 billion solar masses.[28]
- Intermediate-mass black holes, whose sizes are measured in thousands of solar masses, probably exist. They have been proposed as a possible power source for the ultra-luminous X ray sources. There is no known mechanism for them to form directly, so they most probably form via collisions of lower mass black holes, either in the dense stellar cores of globular clusters or galaxies. Such creation events should produce intense bursts of gravitational waves, which may be observed in the near- to mid-term. The boundary limit between super- and intermediate-mass black holes is a matter of convention. Their lower mass limit, the maximum mass for direct formation of a single black hole from collapse of a massive star, is poorly known at present.
- Stellar-mass black holes have masses ranging from a lower limit of about 1.5–3.0 solar masses (the Tolman-Oppenheimer-Volkoff limit for the maximum mass of neutron stars) up to perhaps 15–20 solar masses, and are created by the collapse of individual stars, or by the coalescence (inevitable, due to gravitational radiation) of binary neutron stars. Stars may form with initial masses up to ≈100 solar masses, or possibly even higher, but these shed most of their outer massive layers during earlier phases of their evolution, either blown away in stellar winds during the red giant, AGB, and Wolf-Rayet stages, or expelled in supernova explosions for stars that turn into neutron stars or black holes. Being known mostly by theoretical models for late-stage stellar evolution, the upper limit for the mass of stellar-mass black holes is somewhat uncertain at present. The cores of still lighter stars form white dwarfs.
- Micro black holes (also mini black holes) have masses much less than that of a star. At these sizes, the effects of quantum mechanics are expected to come into play. There is no known mechanism for them to form via normal processes of stellar evolution, but certain inflationary scenarios predicted their production during the early stages of the evolution of the universe. According to some theories of quantum gravity they may also be produced in the highly energetic reaction produced by cosmic rays hitting the atmosphere or even in particle accelerators such as the Large Hadron Collider. The theory of Hawking radiation predicts that such black holes will evaporate in bright flashes of gamma radiation. NASA's Fermi Gamma-ray Space Telescope satellite (formerly GLAST), launched in 2008, will search for such flashes as one of its scientific objectives.
Features
Event horizon
The defining feature of a black hole is the event horizon, a surface in spacetime that marks a point of no return. Once an object crosses this surface, it cannot return to the other side. Consequently, anything inside this surface is completely hidden from outside observers. Other than this, the event horizon is a completely normal part of space with no special features that would allow someone falling into the black hole to know when they would cross the horizon. The event horizon is not a solid surface, and does not obstruct or slow down matter or radiation that is traveling towards the region within the event horizon.
Outside the event horizon, the gravitational field is identical to the field produced by any other spherically symmetric object of the same mass. The popular conception of black holes as "sucking" things in is misleading: objects can orbit black holes indefinitely, provided they stay outside the photon sphere (described below), and also ignoring the effects of gravitational radiation which causes orbiting objects to lose energy (similar to the effect of electromagnetic radiation).
Singularity
According to general relativity, there is a space-time singularity at the center of a spherical black hole, which means an infinite space-time curvature. It means that, from the viewpoint of an observer falling into a black hole, in a finite time (at the end of his fall) a black hole's mass becomes entirely compressed into a region with zero volume, so its density becomes infinite. This zero-volume, infinitely dense region at the center of a black hole is called a gravitational singularity.
The singularity in a non-rotating black hole is a point, in other words it has zero length, width, and height. The singularity of a rotating black hole is smeared out to form a ring shape lying in the plane of rotation. The ring still has no thickness and hence no volume.
The appearance of singularities in general relativity is commonly perceived as signaling the breakdown of the theory. This breakdown is not unexpected, as it occurs in a situation where quantum mechanical effects should become important, since densities are high and particle interactions should thus play a role. Unfortunately, to date it has not been possible to combine quantum and gravitation effects in a single theory. It is however quite generally expected that a theory of quantum gravity will feature black holes without singularities.
Formation of the singularity takes a finite (and very short) time only from the viewpoint of an infalling observer. From the standpoint of a distant observer, it takes infinite time to do so due to gravitational time dilation.
Photon sphere
The photon sphere is a spherical boundary of zero thickness such that photons moving along tangents to the sphere will be trapped in a circular orbit. For non-rotating black holes, the photon sphere has a radius 1.5 times the Schwarzschild radius. The orbits are dynamically unstable, hence any small perturbation (maybe caused by some infalling matter) will grow over time, either setting it on an outward trajectory escaping the black hole or on an inward spiral eventually crossing the event horizon.
While light can still escape from inside the photon sphere, any light that crosses the photon sphere on an inbound trajectory will be captured by the black hole. Hence any light reaching an outside observer from inside the photon sphere must have been emitted by objects inside the photon sphere but still outside of the event horizon.
Other compact objects, such as neutron stars, can also have photon spheres.[29] This follows from the fact gravitation field of an object does not depend on its actual size, hence any object that is smaller than 1.5 times the Schwarzschild radius corresponding to its mass will in fact have a photon sphere.
Ergosphere
![](http://upload.wikimedia.org/wikipedia/commons/thumb/b/b2/Ergosphere_of_a_rotating_black_hole.svg/250px-Ergosphere_of_a_rotating_black_hole.svg.png)
Rotating black holes are surrounded by a region of spacetime in which it is impossible to stand still, called the ergosphere. This is the result of a process known as frame-dragging; general relativity predicts that any rotating mass will tend to slightly "drag" along the spacetime immediately surrounding it. Any object near the rotating mass will tend to start moving in the direction of rotation. For a rotating black hole this effect becomes so strong near the event horizon that an object would have to move faster than the speed of light in the opposite direction to just stand still.
The ergosphere of black hole is bounded by
- on the outside, an oblate spheroid, which coincides with the event horizon at the poles and is noticeably wider around the "equator". This boundary is sometimes called the "ergosurface", but it is just a boundary and has no more solidity than the event horizon. At points exactly on the ergosurface, spacetime is "dragged around at the speed of light."
- on the inside, the (outer) event horizon.
Within the ergosphere, space-time is dragged around faster than light—general relativity forbids material objects to travel faster than light (so does special relativity), but allows regions of space-time to move faster than light relative to other regions of space-time.
Objects and radiation (including light) can stay in orbit within the ergosphere without falling to the center. But they cannot hover (remain stationary, as seen by an external observer), because that would require them to move backwards faster than light relative to their own regions of space-time, which are moving faster than light relative to an external observer.
Objects and radiation can also escape from the ergosphere. In fact the Penrose process predicts that objects will sometimes fly out of the ergosphere, obtaining the energy for this by "stealing" some of the black hole's rotational energy. If a large total mass of objects escapes in this way, the black hole will spin more slowly and may even stop spinning eventually.
Hawking radiation
In 1974, Stephen Hawking showed that black holes are not entirely black but emit small amounts of thermal radiation.[30] He got this result by applying quantum field theory in a static black hole background. The result of his calculations is that a black hole should emit particles in a perfect black body spectrum. This effect has become known as Hawking radiation. Since Hawking's result many others have verified the effect through various methods.[31]
The temperature of the emitted black body spectrum is proportional to the surface gravity of the black hole. For a Schwarzschild black hole this is inversely proportional to the mass. Consequently, large black holes are very cold and emit very little radiation. A stellar black hole of 10 solar masses, for example, would have a Hawking temperature of several nanokelvins, much less than the 2.7 K produced by the cosmic microwave background. Micro black holes on the other hand could be quite bright producing high energy gamma rays.
Due to low Hawking temperature of stellar black holes, Hawking radiation has never been observed at any of the black hole candidates.
Effects of falling into a black hole
This section describes what happens when something falls into a Schwarzschild (i.e. non-rotating and uncharged) black hole. Rotating and charged black holes have some additional complications when falling into them, which are not treated here.
Spaghettification
An object in any very strong gravitational field feels a tidal force stretching it in the direction of the object generating the gravitational field. This is because the inverse square law causes nearer parts of the stretched object to feel a stronger attraction than farther parts. Near black holes, the tidal force is expected to be strong enough to deform any object falling into it, even atoms or composite nucleons; this is called spaghettification.
The strength of the tidal force of a black hole depends on how gravitational attraction changes with distance, rather than on the absolute force being felt. This means that small black holes cause spaghettification while infalling objects are still outside their event horizons, whereas objects falling into large, supermassive black holes may not be deformed or otherwise feel excessively large forces before passing the event horizon.
Before the falling object crosses the event horizon
An object in a gravitational field experiences a slowing down of time, called gravitational time dilation, relative to observers outside the field. The outside observer will see that physical processes in the object, including clocks, appear to run slowly. As a test object approaches the event horizon, its gravitational time dilation (as measured by an observer far from the hole) would approach infinity. Its time would appear to be stopped.
From the viewpoint of a distant observer, an object falling into a black hole appears to slow down, approaching but never quite reaching the event horizon: and it appears to become redder and dimmer, because of the extreme gravitational red shift caused by the gravity of the black hole. Eventually, the falling object becomes so dim that it can no longer be seen, at a point just before it reaches the event horizon. All of this is a consequence of time dilation: the object's movement is one of the processes that appear to run slower and slower, and the time dilation effect is more significant than the acceleration due to gravity; the frequency of light from the object appears to decrease, making it look redder, because the light appears to complete fewer cycles per "tick" of the observer's clock; lower-frequency light has less energy and therefore appears dimmer, as well as redder.
From the viewpoint of the falling object, distant objects generally appear blue-shifted due to the gravitational field of the black hole. This effect may be partly (or even entirely) negated by the red shift caused by the velocity of the infalling object with respect to the object in the distance.
As the object passes through the event horizon
From the viewpoint of the falling object, nothing particularly special happens at the event horizon. In fact, there is no (local) way for him to find out whether he has passed the horizon or not. An infalling object takes a finite proper time (i.e. measured by its own clock) to fall past the event horizon. This in contrast with the infinite amount of time it takes for a distant observer to see the infalling object cross the horizon.
Inside the event horizon
The object reaches the singularity at the center within a finite amount of proper time, as measured by the falling object. An observer on the falling object would continue to see objects outside the event horizon, blue-shifted or red-shifted depending on the falling object's trajectory.
The amount of proper time a faller experiences below the event horizon depends upon where they started from rest, with the maximum being for someone who starts from rest at the event horizon. A paper in 2007 examined the effect of firing a rocket pack within the black hole, showing that this can only reduce the proper time of a person who starts from rest at the event horizon. However, for anyone else, a judicious burst of the rocket can extend the lifetime of the faller, but overdoing it will again reduce the proper time experienced. However, this cannot prevent the inevitable collision with the central singularity.[32]
Hitting the singularity
As an infalling object approaches the singularity, tidal forces acting on it approach infinity. All components of the object, including atoms and subatomic particles, are torn away from each other before striking the singularity. At the singularity itself, effects are unknown; it is believed that a theory of quantum gravity is needed to accurately describe events near it.
Formation and evolution
From the exotic nature of black holes, it is natural to question if such bizarre objects could actually exist in nature or that they are merely pathological solutions to Einstein's equations. However in 1970, Hawking and Penrose proved the opposite; under generic conditions black holes are expected to form in any universe.[33] The primary formation process for black holes is expected to be the gravitational collapse of heavy objects such as stars, but there are also more exotic processes that can lead to the production of black holes.
Gravitation collapse
Gravitational collapse occurs when an object's internal pressure is insufficient to resist the object's own gravity. For stars this usually occurs either because a star has too little "fuel" left to maintain its temperature, or because a star which would have been stable receives a lot of extra matter in a way which does not raise its core temperature. In either case the star's temperature is no longer high enough to prevent it from collapsing under its own weight (the ideal gas law explains the connection between pressure, temperature, and volume).
The collapse may be stopped by the degeneracy pressure of the star's constituents, condensing the matter in an exotic denser state. The result is one of the various types of compact star. Which type of compact star is formed depends on the mass of the remnant - the matter left over after changes triggered by the collapse (such as supernova or pulsations leading to a planetary nebula) have blown away the outer layers. Note that this can be substantially less than the original star - remnants exceeding 5 solar masses are produced by stars which were over 20 solar masses before the collapse.
If the mass of the remnant exceeds ~3-4 solar masses (the Tolman-Oppenheimer-Volkoff limit)—either because the original star was very heavy or because the remnant collected additional mass through accretion of matter)—even the degeneracy pressure of neutrons is insufficient to stop the collapse. After this no known mechanism (except maybe the quark degeneracy pressure, see quark star) is powerful enough to stop the collapse and the object will inevitably collapse to a black hole.
This gravitational collapse of heavy stars is assumed to be responsible for the formation of most (if not all) stellar mass black holes.
Creation of primordial black holes in the big bang
Gravitational collapse requires great densities. In the current epoch of the universe these high densities are only found in stars, but in the early universe shortly after the big bang densities were much greater, possibly allowing for the creation of black holes. The high density alone is not enough to allow the formation of black holes since a uniform mass distribution will not allow the mass to bunch up. In order for primordial black holes to form in such a dense medium, there must be initial density perturbations which can then grow under their own gravity. Different models for the early universe vary widely in their predictions of the size of these perturbations. Various models predict the creation of black holes, ranging from a Planck mass to hundreds of thousands of solar masses.[34] Primordial black holes could thus account for the creation of any type of black hole.
Production in high energy collisions
Gravitational collapse is not the only process that could create black holes. In principle, black holes could also be created in high energy collisions that create sufficient density. Since classically black holes can take any mass, one would expect micro black holes to be created in any such process no matter how low the energy. However, to date, no such events have ever been detected either directly or indirectly as a deficiency of the mass balance in particle accelerator experiments.[35] This suggests that there must be a lower limit for the mass of black holes.
Theoretically this boundary is expected to lie around the Planck mass (~1019 GeV/c2), where quantum effects are expected to make the theory of general relativity break down completely.[citation needed] This would put the creation of black holes firmly out of reach of any high energy process occurring on or near the Earth. Certain developments in quantum gravity however suggest that this bound could be much lower. Some braneworld scenarios for example put the Planck mass much lower, may be even as low as 1 TeV.[36] This would make it possible for micro black holes to be created in the high energy collisions occurring when cosmic rays hit the Earth's atmosphere, or even maybe in the new Large Hadron Collider at CERN. These theories are however very speculative, and the creation of black holes in these processes is deemed unlikely by many specialists.
Growth
Once a black hole has formed, it can continue to grow by absorbing additional matter. Any black hole will continually absorb interstellar dust from its direct surroundings and omnipresent cosmic background radiation, but neither of these processes should significantly affect the mass of a stellar black hole. More significant contributions can occur when the black hole formed in a binary star system. After formation the black hole can then leech significant amounts of matter from its companion.
Much larger contributions can be obtained when a black hole merges with other stars or compact objects. The supermassive black holes suspected in the center of most galaxies are expected to have formed from the coagulation of many smaller objects. The process has also been proposed as the origin of some intermediate-mass black holes.
Evaporation
If Hawking's theory of black hole radiation is correct then black holes are expected to emit a thermal spectrum of radiation, and thereby lose mass, because according to the theory of relativity mass is just highly condensed energy (E = mc2).[30] Black holes will thus shrink and evaporate over time. The temperature of this spectrum (Hawking temperature) is proportional to the surface gravity of the black hole, which in turn is inversely proportional to the mass. Large black holes thus emit less radiation than small black holes.
A stellar black hole of 5 solar masses has a Hawking temperature of about 12 nanokelvins. This is far less than the 2.7 K produced by the cosmic microwave background. Stellar mass (and larger) black holes thus receive more mass from the CMB than they emit through Hawking radiation and will thus grow instead of shrink. In order to have a Hawking temperature larger than 2.7 K (and thus be able to evaporate) a black hole needs to be lighter than the Moon (and thus have diameter of less than a tenth of a millimeter).
On the other hand if a black hole is very small the radiation effects are expected to become very strong. Even a black hole that is heavy compared to a human would evaporate in an instant. A black hole the weight of a car (~10−24 m) would only take a nanosecond to evaporate, during which time it would briefly have a luminosity more than 200 times that of the sun. Lighter black holes are expected to evaporate even faster, for example a black hole of mass 1 TeV/c2 would take less than 10−88 seconds to evaporate completely. Of course, for such a small black hole quantum gravitation effects are expected to play an important role and could even – although current developments in quantum gravity do not indicate so – hypothetically make such a small black hole stable.
Techniques for finding black holes
Accretion disks and gas jets
![](http://upload.wikimedia.org/wikipedia/commons/thumb/a/ab/Black_hole_jet_diagram.jpg/220px-Black_hole_jet_diagram.jpg)
Most accretion disks and gas jets are not clear proof that a stellar-mass black hole is present, because other massive, ultra-dense objects such as neutron stars and white dwarfs cause accretion disks and gas jets to form and to behave in the same ways as those around black holes. But they can often help by telling astronomers where it might be worth looking for a black hole.
On the other hand, extremely large accretion disks and gas jets may be good evidence for the presence of supermassive black holes, because as far as we know any mass large enough to power these phenomena must be a black hole.
Strong radiation emissions
![](http://upload.wikimedia.org/wikipedia/commons/thumb/b/ba/Black_hole_quasar_NASA.jpg/220px-Black_hole_quasar_NASA.jpg)
Steady X-ray and gamma ray emissions also do not prove that a black hole is present, but can tell astronomers where it might be worth looking for one - and they have the advantage that they pass fairly easily through nebulae and gas clouds.
But strong, irregular emissions of X-rays, gamma rays and other electromagnetic radiation can help to prove that a massive, ultra-dense object is not a black hole, so that "black hole hunters" can move on to some other object. Neutron stars and other very dense stars have surfaces, and matter colliding with the surface at a high percentage of the speed of light will produce intense flares of radiation at irregular intervals. Black holes have no material surface, so the absence of irregular flares around a massive, ultra-dense object suggests that there is a good chance of finding a black hole there.
Intense but one-time gamma ray bursts (GRBs) may signal the birth of "new" black holes, because astrophysicists think that GRBs are caused either by the gravitational collapse of giant stars[37] or by collisions between neutron stars,[38] and both types of event involve sufficient mass and pressure to produce black holes. But it appears that a collision between a neutron star and a black hole can also cause a GRB,[39] so a GRB is not proof that a "new" black hole has been formed. All known GRBs come from outside our own galaxy, and most come from billions of light years away[40] so the black holes associated with them are actually billions of years old.
Some astrophysicists believe that some ultraluminous X-ray sources may be the accretion disks of intermediate-mass black holes.[41]
Quasars are thought to be the accretion disks of supermassive black holes, since no other known object is powerful enough to produce such strong emissions. Quasars produce strong emission across the electromagnetic spectrum, including UV, X-rays and gamma-rays and are visible at tremendous distances due to their high luminosity. Between 5 and 25% of quasars are "radio loud," so called because of their powerful radio emission.[42]
Gravitational lensing
![](http://upload.wikimedia.org/wikipedia/commons/thumb/0/03/Black_hole_lensing_web.gif/170px-Black_hole_lensing_web.gif)
A gravitational lens is formed when the light from a very distant, bright source (such as a quasar) is "bent" around a massive object (such as a black hole) between the source object and the observer. The process is known as gravitational lensing, and is one of the predictions of the general theory of relativity. According to this theory, mass "warps" space-time to create gravitational fields and therefore bend light as a result.
A source image behind the lens may appear as multiple images to the observer. In cases where the source, massive lensing object, and the observer lie in a straight line, the source will appear as a ring behind the massive object.
Gravitational lensing can be caused by objects other than black holes, because any very strong gravitational field will bend light rays. Some of these multiple-image effects are probably produced by distant galaxies.
Objects orbiting possible black holes
| author=Staff | date=August 30, 2006 | url=http://chandra.harvard.edu/photo/2003/bhspin/more.html | title=More Images of Cygnus X-1, XTE J1650-500 & GX 339-4 | publisher=Harvard-Smithsonian Center for Astrophysics/Chandra X-ray Center | accessdate=2008-03-30 }}</ref>]]
Objects orbiting black holes probe the gravitational field around the central object. An early example, discovered in the 1970s, is the accretion disk orbiting the putative black hole responsible for Cygnus X-1, a famous X-ray source. While the material itself cannot be seen directly, the X rays flicker on a millisecond time scale, as expected for hot clumpy material orbiting a ~10 solar-mass black hole just prior to accretion. The X-ray spectrum exhibits the characteristic shape expected for a disk of orbiting relativistic material, with an iron line, emitted at ~6.4 keV, broadened to the red (on the receding side of the disk) and to the blue (on the approaching side).
Another example is the star S2, seen orbiting the Galactic center. Here the star is several light hours from the ~3.5×106 solar mass black hole, so its orbital motion can be plotted. Nothing is observed at the center of the observed orbit, the position of the black hole itself—as expected for a black object.
Determining the mass of black holes
Quasi-periodic oscillations can be used to determine the mass of black holes.[43] The technique uses a relationship between black holes and the inner part of their surrounding disks, where gas spirals inward before reaching the event horizon. As the gas collapses inwards, it radiates X-rays with an intensity that varies in a pattern that repeats itself over a nearly regular interval. This signal is the Quasi-Periodic Oscillation, or QPO. A QPO’s frequency depends on the black hole’s mass; the event horizon lies close in for small black holes, so the QPO has a higher frequency. For black holes with a larger mass, the event horizon is farther out, so the QPO frequency is lower.
Black hole candidates
Supermassive black holes at the centers of galaxies
![](http://upload.wikimedia.org/wikipedia/commons/thumb/3/39/M87_jet.jpg/284px-M87_jet.jpg)
According to the American Astronomical Society, every large galaxy has a supermassive black hole at its center.[citation needed] The black hole’s mass is proportional to the mass of the host galaxy, suggesting that the two are linked very closely. The Hubble Space Telescope and ground-based telescopes in Hawaii were used in a large survey of galaxies.
For decades, astronomers have used the term "active galaxy" to describe galaxies with unusual characteristics, such as unusual spectral line emission and very strong radio emission.[44][45] However, theoretical and observational studies have shown that the active galactic nuclei (AGN) in these galaxies may contain supermassive black holes.[44][45] The models of these AGN consist of a central black hole that may be millions or billions of times more massive than the Sun; a disk of gas and dust called an accretion disk; and two jets that are perpendicular to the accretion disk.[45]
Although supermassive black holes are expected to be found in most AGN, only some galaxies' nuclei have been more carefully studied in attempts to both identify and measure the actual masses of the central supermassive black hole candidates. Some of the most notable galaxies with supermassive black hole candidates include the Andromeda Galaxy, M32, M87, NGC 3115, NGC 3377, NGC 4258, and the Sombrero Galaxy.[46]
Astronomers are confident that our own Milky Way galaxy has a supermassive black hole at its center, in a region called Sagittarius A*:
- A star called S2 (star) follows an elliptical orbit with a period of 15.2 years and a pericenter (closest) distance of 17 light hours from the central object.
- The first estimates indicated that the central object contains 2.6 million solar masses and has a radius of less than 17 light hours. Only a black hole can contain such a vast mass in such a small volume.
- Further observations[47] strengthened the case for a black hole, by showing that the central object's mass is about 3.7 million solar masses and its radius no more than 6.25 light-hours.
Intermediate-mass black holes in globular clusters
In 2002, the Hubble Space Telescope produced observations indicating that globular clusters named M15 and G1 may contain intermediate-mass black holes.[48][49] This interpretation is based on the sizes and periods of the orbits of the stars in the globular clusters. But the Hubble evidence is not conclusive, since a group of neutron stars could cause similar observations. Until recent discoveries, many astronomers thought that the complex gravitational interactions in globular clusters would eject newly-formed black holes.
In November 2004 a team of astronomers reported the discovery of the first well-confirmed intermediate-mass black hole in our Galaxy, orbiting three light-years from Sagittarius A*. This black hole of 1,300 solar masses is within a cluster of seven stars, possibly the remnant of a massive star cluster that has been stripped down by the Galactic Centre.[50][51] This observation may add support to the idea that supermassive black holes grow by absorbing nearby smaller black holes and stars.
In January 2007, researchers at the University of Southampton in the United Kingdom reported finding a black hole, possibly of about 10 solar masses, in a globular cluster associated with a galaxy named NGC 4472, some 55 million light-years away.[52][53]
Stellar-mass black holes in the Milky Way
![](http://upload.wikimedia.org/wikipedia/commons/thumb/2/2a/Accretion_disk.jpg/325px-Accretion_disk.jpg)
Our Milky Way galaxy contains several probable stellar-mass black holes which are closer to us than the supermassive black hole in the Sagittarius A* region. These candidates are all members of X-ray binary systems in which the denser object draws matter from its partner via an accretion disk. The probable black holes in these pairs range from three to more than a dozen solar masses.[54][55] The most distant stellar-mass black hole ever observed is a member of a binary system located in the Messier 33 galaxy.[56]
Micro black holes
There is theoretically no smallest size for a black hole. Once created, it has the properties of a black hole. Stephen Hawking theorized that primordial black holes could evaporate and become even tinier, i.e. micro black holes. Searches for evaporating primordial black holes are proposed for the Fermi Gamma-ray Space Telescope, which was launched on June 11, 2008. However, if micro black holes can be created by other means, such as by cosmic ray impacts or in colliders, that does not imply that they must evaporate.
The formation of black hole analogs on Earth in particle accelerators has been reported. These black hole analogs are not the same as gravitational black holes, but they are vital testing grounds for quantum theories of gravity.[57]
They act like black holes because of the correspondence between the theory of the strong nuclear force, which has nothing to do with gravity, and the quantum theory of gravity. They are similar because both are described by string theory. So the formation and disintegration of a fireball in quark gluon plasma can be interpreted in black hole language. The fireball at the Relativistic Heavy Ion Collider [RHIC] is a phenomenon which is closely analogous to a black hole, and many of its physical properties can be correctly predicted using this analogy. The fireball, however, is not a gravitational object. It is presently unknown whether the much more energetic Large Hadron Collider [LHC] would be capable of producing the speculative large extra dimension micro black hole, as many theorists have suggested. See Safety of particle collisions at the Large Hadron Collider for a more in depth discussion.
History
The Newtonian conceptions of Michell and Laplace are often referred to as "dark stars" to distinguish them from the "black holes" of general relativity.
Newtonian theories
The concept of a body so massive that even light could not escape was put forward by the geologist John Michell in a letter written to Henry Cavendish in 1783 and published by the Royal Society.[5]
“ | If the semi-diameter of a sphere of the same density as the Sun were to exceed that of the Sun in the proportion of 500 to 1, a body falling from an infinite height towards it would have acquired at its surface greater velocity than that of light, and consequently supposing light to be attracted by the same force in proportion to its vis inertiae, with other bodies, all light emitted from such a body would be made to return towards it by its own proper gravity. | ” |
This assumes that light is influenced by gravity in the same way as massive objects.
In 1796, the mathematician Pierre-Simon Laplace promoted the same idea in the first and second editions of his book Exposition du système du Monde (it was removed from later editions).
The idea of black holes was largely ignored in the nineteenth century, since light was then thought to be a massless wave and therefore not influenced by gravity. Unlike a modern black hole, the object behind the horizon is assumed to be stable against collapse.
Theories based on general relativity
In 1915, Albert Einstein developed the theory of gravity called general relativity, having earlier shown that gravity does influence light (although light has zero rest mass, it is not the rest mass that is the source of gravity but the energy). A few months later, Karl Schwarzschild gave the solution for the gravitational field of a point mass and a spherical mass,[24] showing that a black hole could theoretically exist. The Schwarzschild radius is now known to be the radius of the event horizon of a non-rotating black hole, but this was not well understood at that time, for example Schwarzschild himself thought it was not physical. Johannes Droste, a student of Lorentz, independently gave the same solution for the point mass a few months after Schwarzschild and wrote more extensively about its properties.
In 1930, the astrophysicist Subrahmanyan Chandrasekhar argued that, according to special relativity, a non-rotating body above 1.44 solar masses (the Chandrasekhar limit), would collapse since there was nothing known at that time could stop it from doing so. His arguments were opposed by Arthur Eddington, who believed that something would inevitably stop the collapse. Eddington was partly right: a white dwarf slightly more massive than the Chandrasekhar limit will collapse into a neutron star. But in 1939, Robert Oppenheimer published papers (with various co-authors) which predicted that stars above about three solar masses (the Tolman-Oppenheimer-Volkoff limit) would collapse into black holes for the reasons presented by Chandrasekhar.[58]
Oppenheimer and his co-authors used Schwarzschild's system of coordinates (the only coordinates available in 1939), which produced mathematical singularities at the Schwarzschild radius, in other words the equations broke down at the Schwarzschild radius because some of the terms were infinite. This was interpreted as indicating that the Schwarzschild radius was the boundary of a "bubble" in which time "stopped". For a few years the collapsed stars were known as "frozen stars" because the calculations indicated that an outside observer would see the surface of the star frozen in time at the instant where its collapse takes it inside the Schwarzschild radius. But many physicists could not accept the idea of time standing still inside the Schwarzschild radius, and there was little interest in the subject for over 20 years.
In 1958, David Finkelstein broke the deadlock over "stopped time" and introduced the concept of the event horizon by presenting the Eddington-Finkelstein coordinates, which enabled him to show that "The Schwarzschild surface r = 2 m is not a singularity but acts as a perfect unidirectional membrane: causal influences can cross it but only in one direction".[59] Note that at this stage all theories, including Finkelstein's, covered only non-rotating, uncharged black holes.
In 1963, Roy Kerr extended Finkelstein's analysis by presenting the Kerr metric (coordinates) and showing how this made it possible to predict the properties of rotating black holes.[60] In addition to its theoretical interest, Kerr's work made black holes more believable for astronomers, since black holes are formed from stars and all known stars rotate.
In 1967, astronomers discovered pulsars, and within a few years could show that the known pulsars were rapidly rotating neutron stars. Until that time, neutron stars were also regarded as just theoretical curiosities. So the discovery of pulsars awakened interest in all types of ultra-dense objects that might be formed by gravitational collapse.
In 1970, Stephen Hawking and Roger Penrose proved that black holes are a feature of all solutions to Einstein's equations of gravity, not just of Schwarzschild's, and therefore black holes cannot be avoided in some collapsing objects.[33]
In 1971, Louise Webster and Paul Murdin, at the Royal Greenwich Observatory,[61] and Charles Thomas Bolton, working independently at the University of Toronto's David Dunlap Observatory,[62] observed HDE 226868 wobble, as if orbiting around an invisible but massive companion. Further analysis led to the declaration that the companion, Cygnus X-1, was in fact a black hole.[63][64]
Alternative models
Several alternative models, which behave like a black hole but avoid the singularity, have been proposed. However, most researchers judge these concepts artificial, as they are more complicated but do not give near term observable differences from black holes (see Occam's razor). The most prominent alternative theory is the Gravastar.
In March 2005, physicist George Chapline at the Lawrence Livermore National Laboratory in California proposed that black holes do not exist, and that objects currently thought to be black holes are actually dark-energy stars. He draws this conclusion from some quantum mechanical analyses.[65] Although his proposal currently has little support in the physics community, it was widely reported by the media.[65][66] A similar theory about the non-existence of black holes was later developed by a group of physicists at Case Western Reserve University in June 2007.[67][68]
Among the alternate models are magnetospheric eternally collapsing objects,[69][70][71] clusters of elementary particles[72] (e.g., boson stars[73]), fermion balls,[74] self-gravitating, degenerate heavy neutrinos[75] and even clusters of very low mass (~0.04 solar mass) black holes.[72]
More advanced topics
Holographic world
Leonard Susskind and Nobel prizewinner Gerard 't Hooft have suggested that a black hole is a two dimensional object extant in three dimensional space.[76] In addition, they believe these results may indicate a solution to the black hole information-loss paradox and that we live in a holographic world.
Entropy and Hawking radiation
In 1971, Stephen Hawking showed that the total area of the event horizons of any collection of classical black holes can never decrease, even if they collide and swallow each other; that is merge.[77] This is remarkably similar to the Second Law of Thermodynamics, with area playing the role of entropy. As a classical object with zero temperature it was assumed that black holes had zero entropy; if so the second law of thermodynamics would be violated by an entropy-laden material entering the black hole, resulting in a decrease of the total entropy of the universe. Therefore, Jacob Bekenstein proposed that a black hole should have an entropy, and that it should be proportional to its horizon area. Since black holes do not classically emit radiation, the thermodynamic viewpoint seemed simply an analogy, since zero temperature implies infinite changes in entropy with any addition of heat, which implies infinite entropy. However, in 1974, Hawking applied quantum field theory to the curved spacetime around the event horizon and discovered that black holes emit Hawking radiation, a form of thermal radiation, allied to the Unruh effect, which implied they had a positive temperature. This strengthened the analogy being drawn between black hole dynamics and thermodynamics: using the first law of black hole mechanics, it follows that the entropy of a non-rotating black hole is one quarter of the area of the horizon. This is a universal result and can be extended to apply to cosmological horizons such as in de Sitter space. It was later suggested that black holes are maximum-entropy objects, meaning that the maximum possible entropy of a region of space is the entropy of the largest black hole that can fit into it. This led to the holographic principle.
The Hawking radiation reflects a characteristic temperature of the black hole, which can be calculated from its entropy. The more its temperature falls, the more massive a black hole becomes: the more energy a black hole absorbs, the colder it gets. A black hole with roughly the mass of the planet Mercury would have a temperature in equilibrium with the cosmic microwave background radiation (about 2.73 K). More massive than this, a black hole will be colder than the background radiation, and it will gain energy from the background faster than it gives energy up through Hawking radiation, becoming even colder still. However, for a less massive black hole the effect implies that the mass of the black hole will slowly evaporate with time, with the black hole becoming hotter and hotter as it does so. Although these effects are negligible for black holes massive enough to have been formed astronomically, they would rapidly become significant for hypothetical smaller black holes, where quantum-mechanical effects dominate. Indeed, small black holes are predicted to undergo runaway evaporation and eventually vanish in a burst of radiation.
Although general relativity can be used to perform a semi-classical calculation of black hole entropy, this situation is theoretically unsatisfying. In statistical mechanics, entropy is understood as counting the number of microscopic configurations of a system which have the same macroscopic qualities(such as mass, charge, pressure, etc.). But without a satisfactory theory of quantum gravity, one cannot perform such a computation for black holes. Some promise has been shown by string theory, however. There one posits that the microscopic degrees of freedom of the black hole are D-branes. By counting the states of D-branes with given charges and energy, the entropy for certain supersymmetric black holes has been reproduced. Extending the region of validity of these calculations is an ongoing area of research.
Black hole unitarity
An open question in fundamental physics is the so-called information loss paradox, or black hole unitarity paradox. Classically, the laws of physics are the same run forward or in reverse. That is, if the position and velocity of every particle in the universe were measured, we could (disregarding chaos) work backwards to discover the history of the universe arbitrarily far in the past. In quantum mechanics, this corresponds to a vital property called unitarity, which has to do with the conservation of probability.[78]
Black holes, however, might violate this rule. The position under classical general relativity is subtle but straightforward: because of the classical no hair theorem, we can never determine what went into the black hole. However, as seen from the outside, information is never actually destroyed, as matter falling into the black hole takes an infinite time to reach the event horizon.
Ideas about quantum gravity, on the other hand, suggest that there can only be a limited finite entropy (i.e. a maximum finite amount of information) associated with the space near the horizon; but the change in the entropy of the horizon plus the entropy of the Hawking radiation is always sufficient to take up all of the entropy of matter and energy falling into the black hole.
Many physicists are concerned however that this is still not sufficiently well understood. In particular, at a quantum level, is the quantum state of the Hawking radiation uniquely determined by the history of what has fallen into the black hole; and is the history of what has fallen into the black hole uniquely determined by the quantum state of the black hole and the radiation? This is what determinism, and unitarity, would require.
For a long time Stephen Hawking had opposed such ideas, holding to his original 1975 position that the Hawking radiation is entirely thermal and therefore entirely random, containing none of the information held in material the hole has swallowed in the past; this information he reasoned had been lost. However, on 21 July 2004 he presented a new argument, reversing his previous position.[79] On this new calculation, the entropy (and hence information) associated with the black hole escapes in the Hawking radiation itself. However, making sense of it, even in principle, is difficult until the black hole completes its evaporation. Until then it is impossible to relate in a 1:1 way the information in the Hawking radiation (embodied in its detailed internal correlations) to the initial state of the system. Once the black hole evaporates completely, such identification can be made, and unitarity is preserved.
By the time Hawking completed his calculation, it was already very clear from the AdS/CFT correspondence that black holes decay in a unitary way. This is because the fireballs in gauge theories, which are analogous to Hawking radiation, are unquestionably unitary. Hawking's new calculation has not been evaluated by the specialist scientific community, because the methods he uses are unfamiliar and of dubious consistency; but Hawking himself found it sufficiently convincing to pay out on a bet he had made in 1997 with Caltech physicist John Preskill, to considerable media interest.
References
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- ^ "Gamma-rays from Black Holes and Neutron Stars". Goddard Space Flight Center.
- ^ Ronald A. Remillard; Jeffrey E. Mc Clintock (2006). "X-Ray Properties of Black-Hole Binaries". Annual Review of Astronomy and Astrophysics. 44: 49–92. arXiv:astro-ph/0606352. doi:10.1146/annurev.astro.44.051905.092532. S2CID 119417042.
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Further reading
Popular reading
- Ferguson, Kitty (1991). Black Holes in Space-Time. Watts Franklin. ISBN 0-531-12524-6.
- Hawking, Stephen (1988). A Brief History of Time. Bantam Books. ISBN 0-553-38016-8.
- Hawking, Stephen (1996). The Nature of Space and Time. Princeton University Press. ISBN 0-691-03791-2.
{{cite book}}
: Check|isbn=
value: checksum (help); Unknown parameter|coauthors=
ignored (|author=
suggested) (help) - Melia, Fulvio (2003). The Black Hole at the Center of Our Galaxy. Princeton University Press. ISBN 978-0-691-09505-9.
- Melia, Fulvio (2003). The Edge of Infinity: Supermassive Black Holes in the Universe. Cambridge University Press. ISBN 978-0-521-81405-8.
- Pickover, Clifford (1998). Black Holes: A Traveler's Guide. John Wiley & Sons. ISBN 0-471-19704-1.
- Thorne, Kip S. (1994). Black Holes and Time Warps. W. W. Norton & Company. ISBN 0-393-31276-3.
- Stern, Borris (2008). "Blackhole".
University textbooks and monographs
- Carter, B. (1973). "Black hole equilibrium states". In DeWitt, B.S.; DeWitt, C. (eds.). Black Holes.
- Chandrasekhar, Subrahmanyan (1999). Mathematical Theory of Black Holes. Oxford University Press. ISBN 0-19-850370-9.
- Frolov, V.P.; Novikov, I.D. (1998). Black hole physics.
- Hawking, S.W.; Ellis, G.F.R. (1973). Large Scale Structure of space time. Cambridge University Press. ISBN 0521099064.
- Melia, Fulvio (2007). The Galactic Supermassive Black Hole. Princeton U Press. ISBN 978-0-691-13129-0.
- Taylor, Edwin F.; Wheeler, John Archibald (2000). Exploring Black Holes. Addison Wesley Longman. ISBN 0-201-38423-X.
- Thorne, Kip S.; Misner, Charles; Wheeler, John (1973). Gravitation. W. H. Freeman and Company. ISBN 0-7167-0344-0.
- Wald, Robert M. (1992). Space, Time, and Gravity: The Theory of the Big Bang and Black Holes. University of Chicago Press. ISBN 0-226-87029-4.
Research papers
- Hawking, S. (2005). "Information loss in black holes". Physical Review D. 72 (8): 084013. arXiv:hep-th/0507171. doi:10.1103/PhysRevD.72.084013. S2CID 118893360. Stephen Hawking's purported solution to the black hole unitarity paradox, first reported at a conference in July 2004.
- Ghez, A. M. (2005). "Stellar Orbits around the Galactic Center Black Hole". The Astrophysical Journal. 620 (2): 744–757. arXiv:astro-ph/0306130. doi:10.1086/427175. S2CID 8656531. More accurate mass and position for the black hole at the centre of the Milky Way.
- Hughes, Scott A. (2005). "Trust but verify: The case for astrophysical black holes". arXiv:hep-ph/0511217.
{{cite arXiv}}
:|class=
ignored (help) Lecture notes from 2005 SLAC Summer Institute.
External links
- Ghosh, Pallab (2008-12-09). "Black Hole confirmed in Milky Way". BBC News. Retrieved 2009-03-15.
- Yale University Video Lecture: Introduction to Black Holes at Google Video
- Black Holes: Gravity's Relentless Pull - Award-winning interactive multimedia Web site about the physics and astronomy of black holes from the Space Telescope Science Institute
- FAQ on black holes
- Schwarzschild Geometry on Andrew Hamilton’s website
- Tufts University: Student Project (Great Kid's Section)
- Movie of Black Hole Candidate from Max Planck Institute
- UT Brownsville Group Simulates Spinning Black-Hole Binaries
- Black Hole Research News on ScienceDaily
- Weaver, Kimberly (July 2003). "The Galactic Odd Couple". Scientific American. 289 (1): 34–41. doi:10.1038/scientificamerican0703-34. PMID 12840944.
{{cite journal}}
: CS1 maint: date and year (link) - Carr, Bernard J.; Giddings, Steven B. (May 2005). "Quantum Black Holes". Scientific American. 292 (5): 48–55. doi:10.1038/scientificamerican0505-48. PMID 15882021.
- SPACE.com All About Black Holes - News, Features and Interesting Original Videos
- Black Holes Intro - Introduction to Black Holes
- Advanced Mathematics of Black Hole Evaporation
- HowStuffWorks: How Black Holes Work - Easy to consume guide to Black Holes
- Ted Bunn's Black Holes FAQ explains in simple language some other consequences of the way in which black holes bend space-time.
- Is the Mass of Black Holes Limited? - The Future of Things article