Thermodynamics and its quantum correction of non-commutative Schwarichild black hole

Shen Jue; Liu Cheng-Zhou; Zhu Ning-Ning; Tong Yi-Nuo; Yan Chen-Cheng; Xue Ke-Lei

doi:10.7498/aps.68.20191054

Abstract

Black hole thermodynamics establishes a deep and satisfying link to gravity, thermodynamics, and quantum theory. And, the thermodynamic property of black hole is essentially a quantum feature of gravity. In this paper, in order to study the influence of the quantum gravity effect on the quantum properties of black hole, we study the thermodynamics and its quantum correction to a non-commutative black hole. First of all, the temperature of the non-commutative Schwarichild black hole is calculated by using three different methods: surface gravity, tunneling effects and the first law of black hole thermodynamics. It is found that the same hole temperature is obtained by means of the surface gravity and tunneling effects. However, by using the first law of black hole thermodynamics, different results are derived from the first two methods. Therefore, we incline to the result obtained by surface gravity and tunneling effects, and the temperature obtained by the thermodynamic law needs modifying. That is, for the non-commutative black hole, there is a contradiction to the first law of thermodynamics. To calculate the temperature and other thermodynamic quantities for the non-commutative Schwarichild black hole, we use the corrected first law of black hole thermodynamics proposed in the literature. It is found that the black hole temperature derived by the corrected first law is the same as the temperature obtained by the surface gravity and the tunneling model, and the black hole entropy still follows Beckenstein-Hawking area law. Also, the heat capacity of the black hole is obtained and analyzed. It is seen that when the horizon radius and non-commutative parameter satisfy the particular conditions, the heat capacity is positive and the non-commutative black holes are thermodynamically stable. This is a different result from that of the usual Schwarichild black hole. Further, by studying the influence of generalized uncertainty principle on non-commutative black hole thermodynamics, the quantum corrections from generalized uncertainty principle for temperature, entropy and heat capacity of the non-commutative Schwarzschild black hole are given. It is found that with considering this quantum gravity effect, the obtained black hole entropy contains the item of are alogarithm. If the effect of the generalized uncertainty principle is neglected, the corrected black hole entropy can return to that in the usual case of Beckenstein-Hawing area law. Similarly, the corrected black hole temperature and heat capacity can also return to their counterparts in the case of usual Schwarzschild black hole when this quantum gravity effect is ignored.

Keywords:

Authors and contacts

Department of Physics, Shaoxing University, Shaoxing 312000, China

Corresponding author: Liu Cheng-Zhou, czlzj20@aliyun.com

Funds: Project supported by the Natural Science Foundation of Zhejiang Pvovince, China (Grant No. LY14A030001) and the National Natural Science Foundation of China (Grant No. 11373020)

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References

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Cited By

[1]	Hawking S W 1974 Nature 248 30 Google Scholar
[2]	Hawking S W 1975 Commun. Math. Phys. 43 199 Google Scholar
[3]	Bekenstein J D 1973 Phys. Rev. D 7 2333
[4]	Wald R M 2001 Living Rev. Rel. 4 6 Google Scholar
[5]	蔡荣根, 曹利明 2016 科学通报 61 2083 Cai R G, Cao L M 2016 Chin. Sci. Bull. 61 2083
[6]	Garay L J 1995 Int. J. Mod. Phys. A 10 145 Google Scholar
[7]	Maggiore M 1993 Phys. Lett. B 304 65 Google Scholar
[8]	Kempf A, Mangano G, Mann R B 1995 Phys. Rev. D 52 1108 Google Scholar
[9]	Tawfik A, Diab A 2014 Int. J. Mod. Phys. D 23 1430025 Google Scholar
[10]	Chang L N, Minic D, Okamura N, Takeuchi T 2002 Phys. Rev. D 65 125028 Google Scholar
[11]	Li X 2002 Phys. Lett. B 540 9 Google Scholar
[12]	Liu C Z 2008 Sci. China Ser. G: Phys. Mech. Astron. 51 113 Google Scholar
[13]	Gangopadhyay S, Dutta A, Faizal M 2015 EPL 112 20006 Google Scholar
[14]	Li H L, Song D W, Li W 2019 Gen. Relat. Gravit. 51 20 Google Scholar
[15]	Chen D, Wu H, Yang H 2013 Adv. High. Energy Phys. 43 24126
[16]	Zhao R, Zhang S L 2006 Phys. Lett. B 641 318 Google Scholar
[17]	Majumder B 2011 Phys. Lett. B 703 402 Google Scholar
[18]	Banerjee R, Ghosh S 2010 Phys. Lett. B 688 224 Google Scholar
[19]	Medved A J M, Vagenas E C 2004 Phys. Rev. D 70 124021 Google Scholar
[20]	Anacleto M A, Brito F A, Passos E 2015 Phys. Lett. B 749 181 Google Scholar
[21]	Yoon M, Ha J, Kim W 2007 Phys. Rev. D 76 047501 Google Scholar
[22]	Anacleto M A, Bazeia D, Brito F A, Mota-Silva J C 2016 Adv. High. Energy Phys. 11 8465759
[23]	Maluf R V, Neves J C S 2018 Phys. Rev. D 97 104015 Google Scholar
[24]	Casadio R, Nicolini P, da Rocha R 2018 Class. Quant. Grav. 35 185001 Google Scholar
[25]	Myung Y S, Kim Y W, Park Y J 2007 Phys. Lett. B 645 393 Google Scholar
[26]	Witten E 1996 Nucl. Phys. B 460 335 Google Scholar
[27]	Szabo R J 2003 Phys. Rept. 378 207 Google Scholar
[28]	Nasseri F 2005 Gen. Relat. Gravit. 37 2223 Google Scholar
[29]	Nicolini P, Smailagic A, Spallucci E 2006 Phys. Lett. B 632 547 Google Scholar
[30]	Lopez-Dominguez J C, Obregon O, Sabido M, Ramirez C 2006 Phys. Rev. D 74 084024 Google Scholar
[31]	Chaichian M, Tureanu A, Zet G 2008 Phys. Lett. B 660 573 Google Scholar
[32]	Kobakhidze A 2009 Phys. Rev. D 79 047701 Google Scholar
[33]	Nicolini P 2005 J. Phys. A 38 L631 Google Scholar
[34]	Gruppuso A 2005 J. Phys. A 38 2039 Google Scholar
[35]	Cai R G, Wang A 2010 Phys. Lett. B 686 166 Google Scholar
[36]	Nicolini P, Smailagic A, Spallucci E 2006 ESA Spec. Publ. 637 547
[37]	Nozari K, Fazlpour B 2007 Mod. Phys. Lett. A 22 2917 Google Scholar
[38]	Banerjee R, Majhi B R, Samanta S 2008 Phys. Rev. D 77 124035 Google Scholar
[39]	Baneriee R, Majhi B R, Modak S K 2009 Class. Quant. Grav. 26 085010 Google Scholar
[40]	Nozari K, Mehdipour S H 2008 Class. Quant. Grav. 25 175015 Google Scholar
[41]	Myung Y S, Kim Y W, Park Y J 2007 JHEP 0702 012
[42]	Kim W, Son Edwin J, Yoon M 2008 JHEP 0804 042
[43]	Vakili B, Khosravi N, Sepangi H R 2009 Int. J. Mod. Phys. D 18 159 Google Scholar
[44]	Buric M, Madore J 2008 Eur. Phys. J. C 58 347 Google Scholar
[45]	Huang W H, Huang K W 2009 Phys. Lett. B 670 416 Google Scholar
[46]	Nozari K, Mehdipour S H 2009 JHEP 0903 061
[47]	Nozari K, Islamzadeh S 2013 Astrophys. Space. Sci. 347 299 Google Scholar
[48]	Mehdipour S H, Keshavarz A 2012 Europhys. Lett. 9 10002
[49]	Sharif M, Javed W 2011 Can. J. Phys. 89 1027 Google Scholar
[50]	Faizal M, Amorim R G G, Ulhoa S C 2015 Int. J. Mod. Phys. D 27 1850053
[51]	Ma M S, Zhao R 2014 Class. Quantum. Grav. 31 24
[52]	Casadio R, Micu O, Nicolini P 2015 High. Energy Phys. 178 293
[53]	Ali A F, Nafie H, Shalaby M 2012 Europhys. Lett. 100 20004 Google Scholar
[54]	Liu Z Y, Ren J R 2014 Commun. Theor. Phys. 62 819 Google Scholar
[55]	Mu B, Wang P, Yang H 2015 Adv. High. Energy Phys. 2015 1
[56]	Ma H, Li J 2017 Chin. Phys. B 26 60401 Google Scholar
[57]	Chen N S, Zhang J Y 2015 Chin. Phys. B 24 020401 Google Scholar
[58]	Ibungochouba S T 2015 Chin. Phys. B 24 70401 Google Scholar
[59]	Ye B B, Chen J H, Wang Y J 2017 Chin. Phys. B 26 90202 Google Scholar
[60]	刘成周, 邓岳君, 骆叶成 2018 67 060401 Google Scholar Liu C Z, Deng Y J, Luo Y C 2018 Acta Phys. Sin. 67 060401 Google Scholar
[61]	吴迪, 朱晓丹, 吴双清 2014 63 180401 Google Scholar Wu D, Zhu X D, Wu S Q 2014 Acta Phys. Sin. 63 180401 Google Scholar
[62]	Parikh M K, Wilczek F 2000 Phys. Rev. Lett. 85 5042 Google Scholar
[63]	Parikh M K 2004 Int. J. Mod. Phys. D 13 2351 Google Scholar
[64]	Painleve P 1921 C. R. Acad. Sci. (Paris) 173 677
[65]	刘辽, 赵峥 2004 广义相对论(北京: 高等教育出版社) 第109页 Liu L, Zhao Z 2004 General Relativity (Beijing: Higher Education Press) p109 (in Chinese)
[66]	Camellia G A, Arzano M, Procaccini A 2014 Phys. Rev. D 70 107501

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Vol. 68, Issue 20 - 2019-10-20

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