Area and entropy spectra of black holes via an adiabatic invariant

doi:10.1088/1674-1056/21/7/070401

Abstract By considering an adiabatic invariant for black holes, the area and entropy spectra of static spherically-symmetric black holes are investigated. Without using quasi-normal modes of black holes, equally-spaced area and entropy spectra are derived by only utilizing the adiabatic invariant. The spectra for non-charged and charged black holes are calculated, respectively. All these results are consistent with the original Bekenstein spectra.

Keywords: black hole adiabatic invariant area spectrum entropy spectrum

Received: 15 December 2011
Revised: 12 January 2012
Accepted manuscript online:

PACS:	04.70.-s	(Physics of black holes)
	04.70.Dy	(Quantum aspects of black holes, evaporation, thermodynamics)

Fund: Project supported by the National Natural Science Foundation of China (Grant No. 11045005) and the Natural Science Foundation of Zhejiang Province of China (Grant No. Y6090739).

Corresponding Authors: Liu Cheng-Zhou
E-mail: czlbj20@yahoo.com.cn

Cite this article:

Liu Cheng-Zhou(刘成周) Area and entropy spectra of black holes via an adiabatic invariant 2012 Chin. Phys. B 21 070401

[1]	Bekenstein J D 1972 Lett. Nuovo. Cim. 4 737
[2]	Bekenstein J D 1973 Phys. Rev. D 7 2333
[3]	Bekenstein J D 1974 Lett. Nuovo. Cim. 11 467
[4]	Bekenstein J D 1997 arXiv: 9710076 [gr-qc]
[5]	Bekenstein J D 1998 arXiv: 9808028 [gr-qc]
[6]	Hod S 1998 Phys. Rev. Lett. 81 4293
[7]	Hod S 1998 Phys. Rev. D 59 024014
[8]	Maggiore M 2008 Phys. Rev. Lett. 100 141301
[9]	Wang B, Lin C Y and Molina C 2004 Phys. Rev. D 70 064025
[10]	Kunstatter G 2003 Phys. Rev. Lett. 90 161301
[11]	Vagenas E C 2008 J. High Energy Phys. 0811 073
[12]	Medved A J M 2008 Class. Quant. Grav. 25 205014
[13]	Ropotenko K 2010 Phys. Rev. D 82 044037
[14]	Wei S W, Li R, Liu Y X and Ren J R 2009 J. High Energy Phys. 0903 076
[15]	Kothawala D, Padmanabhan T and Sarkar S 2008 Phys. Rev. D 78 104018
[16]	Tanaka T and Tamaki T 2007 Nucl. Phys. B 883 179
[17]	Li W, Xu L and Lu J 2009 Phys. Lett. B 676 177
[18]	Setare M R 2005 Gen. Rel. Grav. 37 1411
[19]	Setare M R and Vagenas E C 2005 Mod. Phys. Lett. A 20 1923
[20]	Majhi B R 2010 Phys. Lett. B 686 49
[21]	Pan Q Y and Jing J L 2005 Chin. Phys. 14 268
[22]	Liu C Z 2011 Mod. Phys. Lett. A 26 2963
[23]	Jing J L and Chen S B 2005 Chin. Phys. 14 683
[24]	Jing J L and Pan Q Y 2006 Chin. Phys. 15 77
[25]	Liu C Z and Zhu J Y 2009 Chin. Phys. B 18 4161
[26]	Chen J H and Wang Y J 2010 Chin. Phys. B 19 060401
[27]	Wei S W, Liu Y X, Yang K and Zhong Y 2010 Phys. Rev. D 81 104042
[28]	Barvinsky A and Kunstatter G 1996 arXiv: 9607030 [gr-qc]
[29]	Barvinsky A, Das S and Kunstatter G 2001 Class. Quant. Grav. 18 4845
[30]	Barvinsky A, Das S and Kunstatter G 2002 Found. Phys. 32 1851
[31]	Barvinsky A, Das S and Kunstatter G 2001 Phys. Lett. B 517 415
[32]	Ropotenko K 2009 Phys. Rev. D 80 044022
[33]	Majhi B R and Vagenas E C 2011 Phys. Lett. B 701 623
[34]	Louko J and Makela J 1996 Phys. Rev. D 54 4982
[35]	Kwon Y and Nam S 2010 Class. Quant. Grav. 27 125007
[36]	Hawking S W 1975 Comm. Math. Phys. 43 199
[37]	Gibbons G W and Hawking S W 1977 Phys. Rev. D 15 2752
[41]	Chowdhury B D 2008 Pramana 70 3
[42]	Akhmedov E T, Khmedova V A and Singleton D 2006 Phys. Lett. B 642
[38]	Srinivasan K and Padmanabh T 1999 Phys. Rev. D 60 024007
[39]	Parikh M K and Wilczek F 2000 Phys. Rev. Lett. 80 5042
[40]	Parikh M K and Wilczek F 2004 Int. J. Mod. Phys. D 13 2351 124
[43]	Umetsu K 2010 Int. J. Mod. Phys. A 25 4123
[44]	Makela J and Repo P 1998 Phys. Rev. D 57 4899

[1]	The shadow and observation appearance of black hole surrounded by the dust field in Rastall theory Xuan-Ran Zhu(朱轩然), Yun-Xian Chen(陈芸仙), Ping-Hui Mou(牟平辉), and Ke-Jian He(何柯腱). Chin. Phys. B, 2023, 32(1): 010401.
[2]	Simulation of the gravitational wave frequency distribution of neutron star-black hole mergers Jianwei Zhang(张见微), Chengmin Zhang(张承民), Di Li(李菂), Xianghan Cui(崔翔翰), Wuming Yang(杨伍明), Dehua Wang(王德华), Yiyan Yang(杨佚沿), Shaolan Bi(毕少兰), and Xianfei Zhang(张先飞). Chin. Phys. B, 2021, 30(12): 120401.
[3]	Holographic heat engine efficiency of hyperbolic charged black holes Wei Sun(孙威) and Xian-Hui Ge(葛先辉). Chin. Phys. B, 2021, 30(10): 109501.
[4]	Thermodynamics and weak cosmic censorship conjecture of charged AdS black hole in the Rastall gravity with pressure Xin-Yun Hu(胡馨匀), Ke-Jian He(何柯健), Zhong-Hua Li(李中华), Guo-Ping Li(李国平). Chin. Phys. B, 2020, 29(5): 050401.
[5]	Conserved quantities and adiabatic invariants of fractional Birkhoffian system of Herglotz type Juan-Juan Ding(丁娟娟), Yi Zhang(张毅). Chin. Phys. B, 2020, 29(4): 044501.
[6]	Discrete symmetrical perturbation and variational algorithm of disturbed Lagrangian systems Li-Li Xia(夏丽莉), Xin-Sheng Ge(戈新生), Li-Qun Chen(陈立群). Chin. Phys. B, 2019, 28(3): 030201.
[7]	A new type of adiabatic invariants for disturbednon-conservative nonholonomic system Xin-Xin Xu(徐鑫鑫), Yi Zhang(张毅). Chin. Phys. B, 2019, 28(12): 120402.
[8]	Thermal properties of regular black hole with electric charge in Einstein gravity coupled to nonlinear electrodynamics Yi-Huan Wei(魏益焕). Chin. Phys. B, 2019, 28(12): 120401.
[9]	Destroying MTZ black holes with test particles Yu Song(宋宇), Hao Tang(唐浩), De-Cheng Zou(邹德成), Cheng-Yi Sun(孙成一), Rui-Hong Yue(岳瑞宏). Chin. Phys. B, 2018, 27(2): 020401.
[10]	Geometry and thermodynamics of smeared Reissner-Nordström black holes in d-dimensional AdS spacetime Bo-Bing Ye(叶伯兵), Ju-Hua Chen(陈菊华), Yong-Jiu Wang(王永久). Chin. Phys. B, 2017, 26(9): 090202.
[11]	Gravitational quasi-normal modes of static R² Anti-de Sitter black holes Hong Ma(马洪), Jin Li(李瑾). Chin. Phys. B, 2017, 26(6): 060401.
[12]	A note on the mass of Kerr-AdS black holes in the off-shell generalized ADT formalism Yi-De Jing(景艺德), Jun-Jin Peng(彭俊金). Chin. Phys. B, 2017, 26(10): 100401.
[13]	Hawking radiation of stationary and non-stationary Kerr–de Sitter black holes T. Ibungochouba Singh. Chin. Phys. B, 2015, 24(7): 070401.
[14]	Concrete quantum tunneling spectrum of Schwarzschild black holes Chen Si-Na (陈斯纳), Zhang Jing-Yi (张靖仪). Chin. Phys. B, 2015, 24(2): 020401.
[15]	Thermodynamics of a two-dimensional charged black holein the geometric framework Han Yi-Wen (韩亦文), Hong Yun (洪云). Chin. Phys. B, 2014, 23(10): 100401.

No Suggested Reading articles found!

Viewed

Full text

Abstract

Cited

Metrics
Related Articles

Area and entropy spectra of black holes via an adiabatic invariant

Cite this article:

Online attention