Spectroscopy via adiabatic covariant action for the Bañados-Teitelboim-Zanelli (BTZ) black hole

doi:10.1088/1674-1056/22/5/050402

Abstract Very recently, via the covariant form of the adiabatic invariant I=f p_idq_i instead of I=∫ p_idq_i, an equally spaced spectroscopy of a Schwarzschild black hole was derived. The emphasis was given to the covariant of results. In this paper, we extend that work in a spherically symmetric spacetime to the case of a rotating Bañados-Teitelboim-Zanelli (BTZ) black hole. It is noteworthy that the adiabatic covariant action I=f p_idq_i gives the same value for the black hole spectroscopy in different coordinates. The result shows that the area spectrum is ΔA=8π l_P², which confirms the initial proposal of Bekenstein. And the result is consistent with that already obtained by other methods.

Keywords: spectroscopy adiabatic covariant action rotating Bañados-Teitelboim-Zanelli (BTZ) black hole

Received: 07 December 2012
Revised: 26 December 2012
Accepted manuscript online:

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

Fund: Project supported by the Scientific Research Foundation of the Education Department of Liaoning Province, China (Grant No. L2011195).

Corresponding Authors: Li Hui-Ling
E-mail: LHL51759@126.com

Cite this article:

Li Hui-Ling (李慧玲), Lin Rong (林榕), Cheng Li-Ying (程丽英) Spectroscopy via adiabatic covariant action for the Bañados-Teitelboim-Zanelli (BTZ) black hole 2013 Chin. Phys. B 22 050402

[1]	Majhi B R and Vagenas E C 2011 Phys. Lett. B 701 623
[2]	Jiang Q Q and Han Y 2012 Phys. Lett. B 718 584
[3]	Akhmedov E T, Akhmedova V, Singleton D 2006 Phys. Lett. B 642 124
[4]	Akhmedova V, Pilling T, Gill A D and Singleton D 2008 Phys. Lett. B 666 269
[5]	Bekenstein J D 1974 Lett. Nuovo Cimento. 11 467
[6]	Bekenstein J D 1973 Phys. Rev. D 7 2333
[7]	Vagenas E C 2008 J. High Energy Phys. 0811 073
[8]	Carlip S 1995 Class. Quantum Grav. 12 2853
[9]	Parikh M K and Wiltzek F 2000 Phys. Rev. Lett. 85 5042
[10]	Parikh M K 2002 Phys. Lett. B 546 189
[11]	Zhang J Y and Zhao Z 2005 Phys. Lett. B 618 14
[12]	Zhang J Y and Zhao Z 2005 Nucl. Phys. B 725 173
[13]	Liu B S and Zhang J Y 2012 Chin. Phys. B 21 070402
[14]	Wu S Q and Jiang Q Q 2006 J. High Energy Phys. 0603 079
[15]	Jiang Q Q, Wu S Q and Cai X 2007 Phys. Lett. B 647 200
[16]	Jiang Q Q, Wu S Q and Cai X 2007 Phys. Rev. D 75 064029
[17]	Vagenas E C 2001 Phys. Lett. B 503 399
[18]	Vagenas E C 2002 Mod. Phys. Lett. A 17 609
[19]	Vagenas E C 2002 Phys. Lett. B 533 302
[20]	Chen D Y, Jiang Q Q and Zu X T 2008 Phys. Lett. B 665 106
[21]	Chen D Y, Yang H T and Zu X T 2008 Eur. Phys. J. C 56 119
[22]	Kerner R and Mann R B 2008 Phys. Lett. B 665 277
[23]	Kerner R and Mann R B 2006 Phys. Rev. D 73 104010
[24]	Kerner R and Mann R B 2007 Phys. Rev. D 75 084022
[25]	Li H L 2010 Eur. Phys. J. C 65 547
[26]	Li H L, Qi W Y and Lin R 2009 Phys. Lett. B 677 332
[27]	Li H L, Lin R and Cheng L Y 2012 Europhys. Lett. 98 30002
[28]	Li H L 2011 Chin. Phys. B 20 030402
[29]	Li R and Ren J R 2008 Phys. Lett. B 661 370
[30]	Li R, Ren J R and Wei S W 2008 Class. Quantum Grav. 25 125016
[31]	Angheben M, Nadalini M, Vanzo L and Zerbini S 2005 J. High Energy Phys. 0505 014
[32]	Zhang L C, Li H F and Zhao R 2010 Europhys. Lett. 89 20008
[33]	Zhao R and Zhang S L 2006 Phys. Lett. B 641 318
[34]	Zhao R, Wu Y Q, Zhang L C and Li H F 2009 Eur. Phys. J. C 60 685
[35]	Lin K and Yang S Z 2009 Phys. Rev. D 79 064035
[36]	Lin K and Yang S Z 2009 Phys. Lett. B 674 127
[37]	Lin K and Yang S Z 2009 Phys. Lett. B 680 506
[38]	Zeng X X, Zhou S W and Liu W B 2012 Chin. Phys. B 21 090402
[39]	Chen J H and Wang Y J 2010 Chin. Phys. B 19 060401
[40]	Shao J Z and Wang Y J 2012 Chin. Phys. B 21 040404
[41]	Lin K and Yang S Z 2011 Chin. Phys. B 20 110403
[42]	Pan W Z, Yang X J and Xie Z K 2011 Chin. Phys. B 20 049701
[43]	Li H L and Yang S Z 2009 Chin. Phys. B 18 4721
[44]	Zhao R, Zhang L C, Wu Y Q and Li H F 2010 Chin. Phys. B 19 010402
[45]	Fang H Z 2010 Chin. Phys. B 19 110506
[46]	Hod S 1998 Phys. Rev. Lett. 81 4293
[47]	Kunstatter G 2003 Phys. Rev. Lett. 90 161301
[48]	Maggiore M 2008 Phys. Rev. Lett. 100 141301
[49]	Liu Y X, Wei S W, Li R and Ren J R 2009 J. High Energy Phys. 0903 076
[50]	Kwon Y and Nam S 2010 Class. Quant. Grav. 27 125007
[51]	Li H L, Lin R and Cheng L Y 2012 Gen. Relativ. Gravit. 44 2865
[52]	Li H L 2012 Chin. Phys. B 21 120401
[53]	Li W, Xu L and Lu J 2009 Phys. Lett. B 676 177
[54]	Chen D Y, Yang H T and Zu X T 2010 Eur. Phys. J. C 69 289
[55]	Zeng X X, Liu X M and Liu W B 2012 Eur. Phys. J. C 72 1967
[56]	Zeng X X and Liu W B 2012 Eur. Phys. J. C 72 1987
[57]	Jiang Q Q and Cai X 2010 J. High Energy Phys. 1011 066
[58]	Liu C Z 2012 Chin. Phys. B 21 070401
[59]	Painlevé P 1921 La mécanique classique et la theorie de la relativité, Compt. Rend. Acad. Sci. (Paris) 173 677

[1]	Polarization Raman spectra of graphene nanoribbons Wangwei Xu(许望伟), Shijie Sun(孙诗杰), Muzi Yang(杨慕紫), Zhenliang Hao(郝振亮), Lei Gao(高蕾), Jianchen Lu(卢建臣), Jiasen Zhu(朱嘉森), Jian Chen(陈建), and Jinming Cai(蔡金明). Chin. Phys. B, 2023, 32(4): 046803.
[2]	Measuring stellar populations, dust attenuation and ionized gas at kpc scales in 10010 nearby galaxies using the integral field spectroscopy from MaNGA Niu Li(李牛) and Cheng Li(李成). Chin. Phys. B, 2023, 32(3): 039801.
[3]	LAMOST medium-resolution spectroscopic survey of binarity and exotic star (LAMOST-MRS-B): Observation strategy and target selection Jiao Li(李蛟), Jiang-Dan Li(李江丹), Yan-Jun Guo(郭彦君), Zhan-Wen Han(韩占文), Xue-Fei Chen(陈雪飞), Chao Liu(刘超), Hong-Wei Ge(葛宏伟), Deng-Kai Jiang(姜登凯), Li-Fang Li(李立芳), Bo Zhang(章博), Jia-Ming Liu(刘佳明), Hao Tian(田浩), Hao-Tong Zhang(张昊彤), Hai-Long Yuan(袁海龙), Wen-Yuan Cui(崔文元),Juan-Juan Ren(任娟娟), Jing-Hao Cai(蔡靖豪), and Jian-Rong Shi(施建荣). Chin. Phys. B, 2023, 32(1): 019501.
[4]	Optical second-harmonic generation of Janus MoSSe monolayer Ce Bian(边策), Jianwei Shi(史建伟), Xinfeng Liu(刘新风), Yang Yang(杨洋), Haitao Yang(杨海涛), and Hongjun Gao(高鸿钧). Chin. Phys. B, 2022, 31(9): 097304.
[5]	High-sensitivity methane monitoring based on quasi-fundamental mode matched continuous-wave cavity ring-down spectroscopy Zhe Li(李哲), Shuang Yang(杨爽), Zhirong Zhang(张志荣), Hua Xia(夏滑), Tao Pang(庞涛),Bian Wu(吴边), Pengshuai Sun(孙鹏帅), Huadong Wang(王华东), and Runqing Yu(余润磬). Chin. Phys. B, 2022, 31(9): 094207.
[6]	Selective formation of ultrathin PbSe on Ag(111) Jing Wang(王静), Meysam Bagheri Tagani, Li Zhang(张力), Yu Xia(夏雨), Qilong Wu(吴奇龙), Bo Li(黎博), Qiwei Tian(田麒玮), Yuan Tian(田园), Long-Jing Yin(殷隆晶), Lijie Zhang(张利杰), and Zhihui Qin(秦志辉). Chin. Phys. B, 2022, 31(9): 096801.
[7]	In situ study of calcite-III dimorphism using dynamic diamond anvil cell Xia Zhao(赵霞), Sheng-Hua Mei(梅升华), Zhi Zheng(郑直), Yue Gao(高悦), Jiang-Zhi Chen(陈姜智), Yue-Gao Liu(刘月高), Jian-Guo Sun(孙建国), Yan Li(李艳), and Jian-Hui Sun(孙建辉). Chin. Phys. B, 2022, 31(9): 096201.
[8]	Combination of spark discharge and nanoparticle-enhanced laser-induced plasma spectroscopy Qing-Xue Li(李庆雪), Dan Zhang(张丹), Yuan-Fei Jiang(姜远飞), Su-Yu Li(李苏宇), An-Min Chen(陈安民), and Ming-Xing Jin(金明星). Chin. Phys. B, 2022, 31(8): 085201.
[9]	Radiation effects of electrons on multilayer FePS₃ studied with laser plasma accelerator Meng Peng(彭猛), Jun-Bo Yang(杨俊波), Hao Chen(陈浩), Bo-Yuan Li(李博源), Xu-Lei Ge(葛绪雷), Xiao-Hu Yang(杨晓虎), Guo-Bo Zhang(张国博), and Yan-Yun Ma(马燕云). Chin. Phys. B, 2022, 31(8): 086102.
[10]	SERS activity of carbon nanotubes modified by silver nanoparticles with different particle sizes Xiao-Lei Zhang(张晓蕾), Jie Zhang(张洁), Yuan Luo(罗元), and Jia Ran(冉佳). Chin. Phys. B, 2022, 31(7): 077401.
[11]	Structural evolution and bandgap modulation of layered β-GeSe₂ single crystal under high pressure Hengli Xie(谢恒立), Jiaxiang Wang(王家祥), Lingrui Wang(王玲瑞), Yong Yan(闫勇), Juan Guo(郭娟), Qilong Gao(高其龙), Mingju Chao(晁明举), Erjun Liang(梁二军), and Xiao Ren(任霄). Chin. Phys. B, 2022, 31(7): 076101.
[12]	Synchronous detection of multiple optical characteristics of atmospheric aerosol by coupled photoacoustic cavity Hua-Wei Jin(靳华伟), Ren-Zhi Hu(胡仁志), Pin-Hua Xie(谢品华), and Ping Luo(罗平). Chin. Phys. B, 2022, 31(6): 060703.
[13]	Generation of stable and tunable optical frequency linked to a radio frequency by use of a high finesse cavity and its application in absorption spectroscopy Yueting Zhou(周月婷), Gang Zhao(赵刚), Jianxin Liu(刘建鑫), Xiaojuan Yan(闫晓娟), Zhixin Li(李志新), Weiguang Ma(马维光), and Suotang Jia(贾锁堂). Chin. Phys. B, 2022, 31(6): 064206.
[14]	Photothermal-chemical synthesis of P-S-H ternary hydride at high pressures Tingting Ye(叶婷婷), Hong Zeng(曾鸿), Peng Cheng(程鹏), Deyuan Yao(姚德元), Xiaomei Pan(潘孝美), Xiao Zhang(张晓), and Junfeng Ding(丁俊峰). Chin. Phys. B, 2022, 31(6): 067402.
[15]	Laser-induced fluorescence experimental spectroscopy and theoretical calculations of uranium monoxide Xi-Lin Bai(白西林), Xue-Dong Zhang(张雪东), Fu-Qiang Zhang(张富强), and Timothy C Steimle. Chin. Phys. B, 2022, 31(5): 053301.

No Suggested Reading articles found!

Viewed

Full text

Abstract

Cited

Metrics
Related Articles

Spectroscopy via adiabatic covariant action for the Bañados-Teitelboim-Zanelli (BTZ) black hole

Cite this article:

Online attention