Self-Regular Black Holes Quantized by means of an Analogue to Hydrogen Atoms

Liu, Chang; Wu, Yu-Mei; Zhang, Yu-Hao; Miao, Yan-Gang

doi:10.1155/2016/5982482

Article
Report number	arXiv:1511.04865
Title	Self-Regular Black Holes Quantized by means of an Analogue to Hydrogen Atoms
Previous title	Quantization of black holes by analogy with hydrogen atoms
Author(s)	Liu, Chang (Nankai U.) ; Miao, Yan-Gang (Nankai U. ; Beijing, Inst. Theor. Phys. ; CERN) ; Wu, Yu-Mei (Nankai U.) ; Zhang, Yu-Hao (Nankai U.)
Publication	2016
Imprint	16 Nov 2015
Number of pages	7
Note	v1: 14 pages, 3 figures; v2: minor revisions and references added; v3: 15 pages, title slightly changed, appendix and reference added; v4: 14 pages, title slightly changed, clarifications added; v5: minor revisions and the final version to appear in Advances in High Energy Physics
In:	Adv. High Energy Phys. 2016 (2016) 5982482
DOI	10.1155/2016/5982482
Subject category	Particle Physics - Theory
Abstract	We suggest a proposal of quantization for black holes that is based on an analogy between a black hole and a hydrogen atom. A self-regular Schwarzschild-AdS black hole is investigated, where the mass density of the extreme black hole is given by the probability density of the ground state of hydrogen atoms and the mass densities of non-extreme black holes are chosen to be the probability densities of excited states with no angular momenta. Consequently, it is logical to accept quantization of mean radii of hydrogen atoms as that of black hole horizons. In this way, quantization of total black hole masses is deduced. Furthermore, the quantum hoop conjecture and the Correspondence Principle are discussed.
Copyright/License	arXiv nonexclusive-distrib. 1.0 publication: © 2016-2025 The Author(s) (License: CC-BY-3.0), sponsored by SCOAP³

$The blue curve corresponds to the relation eq.~\eqref{mr} that gives the relation between the mass and the horizon of the extreme self-regular Schwarzschild-AdS black hole, and the red curve corresponds to the usual relation associated with the ordinary Schwarzschild-AdS black hole. When the horizon radius grows up, the two curves gradually approach, which means that the effect of noncommutativity mainly exists in the near extremal horizon. Here we set $b=5a$, which satisfies the hoop conjecture, see below for the details.$ $The numerical points of eq.~(\ref{m00}) are plotted in blue color, and the fitting curve of eq.~(\ref{r0}) is plotted in red color. The relative error is less than $4\times10^{-5}\%$.$ $Plots of the relations between black hole masses and their horizon radii. The blue, red, orange, and green curves correspond to the cases of $n=1,2,3,4$, respectively, where we set $b/a=5$ which has been verified to satisfy the hoop conjecture, see eq.~(\ref{meanr}).$ Show more plots

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