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The R = T model,^[1] also known as Jackiw–Teitelboim gravity (named after Roman Jackiw and Claudio Teitelboim), is a theory of gravity with dilaton coupling in one spatial and one time dimension. It should not be confused^[2]^[3] with the CGHS model or Liouville gravity. The action is given by

S={\frac {1}{\kappa }}\int d^{2}x\,{\sqrt {-g}}\,\Phi \left(R-\Lambda \right)

The metric in this case is more amenable to analytical solutions than the general 3+1D case though a canonical reduction for the latter has recently been obtained.^[4] For example, in 1+1D, the metric for the case of two mutually interacting bodies can be solved exactly in terms of the Lambert W function, even with an additional electromagnetic field.

By varying with respect to Φ, we get $R=\Lambda$ on shell, which means the metric is either Anti-de Sitter space or De Sitter space depending upon the sign of Λ.

References

^ Mann, Robert; Shiekh, A.; Tarasov, L. (3 Sep 1990). "Classical and quantum properties of two-dimensional black holes". Nuclear Physics. B. 341 (1): 134–154. Bibcode:1990NuPhB.341..134M. doi:10.1016/0550-3213(90)90265-F.
^ Grumiller, Daniel; Kummer, Wolfgang; Vassilevich, Dmitri (October 2002). "Dilaton Gravity in Two Dimensions". Physics Reports. 369 (4): 327–430. arXiv:hep-th/0204253. Bibcode:2002PhR...369..327G. doi:10.1016/S0370-1573(02)00267-3. S2CID 119497628.
^ Grumiller, Daniel; Meyer, Rene (2006). "Ramifications of Lineland". Turkish Journal of Physics. 30 (5): 349–378. arXiv:hep-th/0604049. Bibcode:2006TJPh...30..349G. Archived from the original on 22 August 2011.
^ Scott, T.C.; Zhang, Xiangdong; Mann, Robert; Fee, G.J. (2016). "Canonical reduction for dilatonic gravity in 3 + 1 dimensions". Physical Review D. 93 (8): 084017. arXiv:1605.03431. Bibcode:2016PhRvD..93h4017S. doi:10.1103/PhysRevD.93.084017.

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[1] Mann, Robert; Shiekh, A.; Tarasov, L. (3 Sep 1990). "Classical and quantum properties of two-dimensional black holes". Nuclear Physics. B. 341 (1): 134–154. Bibcode:1990NuPhB.341..134M. doi:10.1016/0550-3213(90)90265-F.

[2] Grumiller, Daniel; Kummer, Wolfgang; Vassilevich, Dmitri (October 2002). "Dilaton Gravity in Two Dimensions". Physics Reports. 369 (4): 327–430. arXiv:hep-th/0204253. Bibcode:2002PhR...369..327G. doi:10.1016/S0370-1573(02)00267-3. S2CID 119497628.

[3] Grumiller, Daniel; Meyer, Rene (2006). "Ramifications of Lineland". Turkish Journal of Physics. 30 (5): 349–378. arXiv:hep-th/0604049. Bibcode:2006TJPh...30..349G. Archived from the original on 22 August 2011.

[4] Scott, T.C.; Zhang, Xiangdong; Mann, Robert; Fee, G.J. (2016). "Canonical reduction for dilatonic gravity in 3 + 1 dimensions". Physical Review D. 93 (8): 084017. arXiv:1605.03431. Bibcode:2016PhRvD..93h4017S. doi:10.1103/PhysRevD.93.084017.

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+The '''''R'' = ''T'' model''',<ref>{{cite journal | last1 = Mann | first1 = Robert | authorlink1 = Robert B. Mann | last2 = Shiekh | first2 = A. | last3 = Tarasov | first3 = L. | date = 3 Sep 1990 | title = Classical and quantum properties of two-dimensional black holes | journal = Nuclear Physics | volume = 341 | issue = 1 | series = B | pages = 134&ndash;154 | doi = 10.1016/0550-3213(90)90265-F | bibcode= 1990NuPhB.341..134M }}</ref> also known as '''Jackiw–Teitelboim gravity''' (named after [[Roman Jackiw]] and [[Claudio Teitelboim]]), is a theory of gravity with [[dilaton]] coupling in one spatial and one time dimension. It should not be confused<ref>{{cite journal | last1 = Grumiller | first1 = Daniel | authorlink1 = Daniel Grumiller | last2 = Kummer | first2 = Wolfgang  | last3 = Vassilevich | first3 = Dmitri | authorlink3 = Dmitri Vassilevich | date = October 2002 | title = Dilaton Gravity in Two Dimensions | journal = Physics Reports | volume = 369 | issue = 4 | pages = 327&ndash;430 | doi = 10.1016/S0370-1573(02)00267-3 | arxiv = hep-th/0204253 | bibcode = 2002PhR...369..327G | s2cid = 119497628 }}</ref><ref>{{cite journal | last1 = Grumiller | first1 = Daniel | authorlink1 = Daniel Grumiller | last2 = Meyer | first2 = Rene | authorlink2 = Rene Meyer | year = 2006 | title = Ramifications of Lineland | journal = [[Turkish Journal of Physics]] | volume = 30 | issue = 5 | pages = 349&ndash;378 | url = http://mistug.tubitak.gov.tr/bdyim/abs.php?dergi=fiz&rak=0604-8 | archiveurl = https://web.archive.org/web/20110822060534/http://mistug.tubitak.gov.tr/bdyim/abs.php?dergi=fiz&rak=0604-8 | archivedate = 22 August 2011 | url-status = dead | arxiv = hep-th/0604049 | bibcode = 2006TJPh...30..349G }}</ref> with the [[CGHS model]] or [[Liouville gravity]]. The action is given by
-The '''R=T model'''<ref>
+:<math>S = \frac{1}{\kappa}\int d^2x\, \sqrt{-g}\, \Phi \left( R - \Lambda  \right)</math>
-{{cite journal | last1        = Mann | first1       = Robert | authorlink1  = Robert B. Mann | last2        = Shiekh | first2       = A. | last3 = Tarasov | first3 = L. | date         = 3 Sep 1990 | title        = Classical and quantum properties of two-dimensional black holes | journal      = Nuclear Physics | volume       = 341 | issue        = 1 | series       = B | pages        = 134&ndash;154 | doi          = 10.1016/0550-3213(90)90265-F | url          = http://www.sciencedirect.com/science?_ob=ArticleURL&_udi=B6TVC-47200F0-25W&_user=10&_coverDate=09/03/1990&_rdoc=7&_fmt=high&_orig=browse&_origin=browse&_zone=rslt_list_item&_srch=doc-info(%23toc%235531%231990%23996589998%23351258%23FLP%23display%23Volume)&_cdi=5531&_sort=d&_docanchor=&view=c&_ct=14&_acct=C000050221&_version=1&_urlVersion=0&_userid=10&md5=a5aa7425ba25ffef424f5a4d2d0c680a&searchtype=a | archiveurl   = http://ccdb4fs.kek.jp/cgi-bin/img_index?8912298 | archivedate  = Dec 1989}}
+The metric in this case is more amenable to analytical solutions than the general 3+1D case though a canonical reduction for the latter has recently been obtained.<ref>{{cite journal|last1=Scott|first1=T.C.|last2=Zhang|first2=Xiangdong|last3=Mann|first3=Robert|last4=Fee|first4=G.J.|title=Canonical reduction for dilatonic gravity in 3 + 1 dimensions|journal=[[Physical Review D]]|volume=93|issue=8|pages=084017|date=2016|doi=10.1103/PhysRevD.93.084017|arxiv=1605.03431|bibcode=2016PhRvD..93h4017S}}</ref> For example, in 1+1D, the metric for the case of two mutually interacting bodies can be solved exactly in terms of the [[Lambert W function#Generalizations|Lambert W function]], even with an additional electromagnetic field.
-</ref>, also known as '''Jackiw&ndash;Teitelboim gravity''' is a theory of gravity with [[dilaton]] coupling in one spatial and one time dimension. It should not be confused<ref>{{cite journal | last1 = Grumiller | first1 = Daniel | authorlink1 = Daniel Grumiller | last2 = Kummer | first2 = Wolfgang | authorlink2 = Wolfgang Kummer | last3 = Vassilevich | first3 = Dmitri | authorlink3 = Dmitri Vassilevich | date = October 2002 | title = Dilaton Gravity in Two Dimensions | journal = Physics Reports | volume = 369 | issue = 4 | pages = 327&ndash;430 | doi = 10.1016/S0370-1573(02)00267-3 | url =http://www.sciencedirect.com/science?_ob=ArticleURL&_udi=B6TVP-46SP0J5-1&_user=10&_coverDate=10/31/2002&_rdoc=1&_fmt=high&_orig=search&_origin=search&_sort=d&_docanchor=&view=c&_acct=C000050221&_version=1&_urlVersion=0&_userid=10&md5=1631f280c7f4234507b308c49b2598e3&searchtype=a|archiveurl = http://arxiv.org/abs/hep-th/0204253 | archivedate = 4 Jan 2008 }}</ref><ref>
-{{cite journal | last1        = Grumiller | first1       = Daniel | authorlink1  = Daniel Grumiller | last2        = Meyer | first2       = Rene | authorlink2  = Rene Meyer | year         = 2006 | title        = Ramifications of Lineland | journal      = Turkish Journal of Physics| volume       = 30 | issue = 5 | pages        = 349&ndash;378 | url          = http://mistug.tubitak.gov.tr/bdyim/abs.php?dergi=fiz&rak=0604-8 | archiveurl   = http://arxiv.org/abs/hep-th/0604049 | archivedate  = 1 June 2006 }}
-</ref> with the [[CGHS model]] or [[Liouville gravity]]. The action is given by
-:<math>S = \frac{1}{\kappa}\int d^2x\, \sqrt{-g}\Phi \left[ -R + \Lambda + \kappa\mathcal{L}_{\text{mat}} \right]</math>
-where &Phi; is the dilaton, and the equation of motion is
-:<math>R-\Lambda=\kappa T</math>
-The metric in this case is more amenable to analytical solutions than the general 3+1D case. For example, in 1+1D, the metric for the case of two mutually interacting bodies can be solved exactly in terms of the [[Lambert_W_function#Generalizations|Lambert W function]], even with an additional electromagnetic field (see [[Quantum_gravity#The_dilaton|quantum gravity]] and references for details) .
-== References ==
-<references />
+By varying with respect to Φ, we get <math>R=\Lambda</math> on shell, which means the metric is either [[Anti-de Sitter space]] or [[De Sitter space]] depending upon the sign of Λ.
 == See also ==
+{{slink|Dilaton#The dilaton in quantum gravity}}
+== References ==
+{{reflist}}
-* [[CGHS model]]
-* [[Liouville gravity]]
-* [[Quantum_gravity#The_dilaton|quantum gravity]]
 {{theories of gravitation}}
 {{quantum gravity}}
+{{DEFAULTSORT:Jackiw-Teitelboim gravity}}
+[[Category:Theory of relativity]]
 {{relativity-stub}}
-[[Category:Relativity]]