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)

FullText HTML : translate this paragraph

References

[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

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

[1]	Aili Mieralimujiang, Mamat Mamatrishat, Ghupur Yasenjan. Thermodynamic properties of harmonic oscillator system in noncommutative phase space. Acta Physica Sinica, 2015, 64(14): 140201. doi: 10.7498/aps.64.140201
[2]	Li He-Ling, Wang Juan-Juan, Yang Bin, Wang Ya-Ni, Shen Hong-Jun. Thermodynamic properties of Fermi gas under generalized uncertainty principle. Acta Physica Sinica, 2015, 64(8): 080502. doi: 10.7498/aps.64.080502
[3]	Zheng Bo-Yu, Dong Hui-Long, Chen Fei-Fan. Characterization of thermal conductivity for GNR based on nonequilibrium molecular dynamics simulation combined with quantum correction. Acta Physica Sinica, 2014, 63(7): 076501. doi: 10.7498/aps.63.076501
[4]	Deng Wei, Fang Jie, Wu Zhen-Jun, Wu Yan-Min. Adaptive modified function projective synchronization of a class of chaotic systems with uncertainties. Acta Physica Sinica, 2012, 61(14): 140503. doi: 10.7498/aps.61.140503
[5]	Huang Hai, He Feng, Sun Hang-Bin. Statistical entropy of reissner-nordstrm-de sitter black hole by generalized uncertainty principle. Acta Physica Sinica, 2012, 61(11): 110403. doi: 10.7498/aps.61.110403
[6]	Zeng Xiao-Xiong. Entropy correction to Kerr-Newman black hole. Acta Physica Sinica, 2010, 59(1): 92-96. doi: 10.7498/aps.59.92
[7]	He Feng, Zhao Fan. Statistical entropy of Gibbons-Maeda black hole computed by generalized uncertainty principle. Acta Physica Sinica, 2009, 58(2): 740-743. doi: 10.7498/aps.58.740
[8]	Cui Da-Jian, Lin De-Hua, Yu Hai-Feng, Peng Zhi-Hui, Zhu Xiao-Bo, Zheng Dong-Ning, Jing Xiu-Nian, Lü Li, Zhao Shi-Ping. Quantum corrections in fitting the switching current distributions of intrinsic Josephson junction. Acta Physica Sinica, 2008, 57(9): 5933-5936. doi: 10.7498/aps.57.5933
[9]	Han Yi-Wen, Hong Yun, Yang Shu-Zheng. The generalized uncertainty relation and Dirac field entropy of black hole with an internal global monopole. Acta Physica Sinica, 2007, 56(1): 10-14. doi: 10.7498/aps.56.10
[10]	Zhou Shi-Wei, Liu Wen-Biao. Thermodynamics of Gibbons-Maeda dilaton black hole and Garfinkle-Horowitz-Strominger dilaton black hole in noncommutative space-time. Acta Physica Sinica, 2007, 56(11): 6767-6771. doi: 10.7498/aps.56.6767
[11]	. Canonical entropy and phase transition of black hole. Acta Physica Sinica, 2007, 56(12): 7355-7358. doi: 10.7498/aps.56.7355
[12]	Zhao Ren, Zhang Li-Chun, Zhang Sheng-Li. Canonical entropy of black hole. Acta Physica Sinica, 2007, 56(7): 3719-3722. doi: 10.7498/aps.56.3719
[13]	Liu Xiao-Ying, Zhang Jia. The generalized uncertainty relation and the thermodynamic quantities near the black holes. Acta Physica Sinica, 2006, 55(11): 5638-5642. doi: 10.7498/aps.55.5638
[14]	Liu Cheng-Zhou, Zhao Zheng. Entanglement entropy of the Gibbons-Maeda dilaton black hole. Acta Physica Sinica, 2006, 55(4): 1607-1615. doi: 10.7498/aps.55.1607
[15]	Liu Cheng-Zhou. Quantum entropy of the general non-stationary black hole with charges. Acta Physica Sinica, 2005, 54(5): 1977-1981. doi: 10.7498/aps.54.1977
[16]	Wang Gang-Zhu, Wang Ji-Long. Quantum thermodynamical properties of the slowly changing nonstationary Kerr-Newman black hole. Acta Physica Sinica, 2004, 53(6): 1669-1674. doi: 10.7498/aps.53.1669
[17]	Li Gu-Qiang. Quantum corrections to the entropy of the Barriola-Vilenkin black hole due to sp in fields. Acta Physica Sinica, 2003, 52(6): 1346-1349. doi: 10.7498/aps.52.1346
[18]	LIN HAI. A NEW ENTROPY OF BLACK HOLE IN ACCORDANCE WITH THE THIRD LAW OF THERMODYNAMICS. Acta Physica Sinica, 2000, 49(8): 1413-1415. doi: 10.7498/aps.49.1413
[19]	LI LI-XIN, LIU LIAO. THE PROPERTIES OF RADIATION NEAR THE BLACK HOLE'S HORIZON AND THE SEDOND LAW OF THERMODYNAMICS. Acta Physica Sinica, 1993, 42(1): 161-168. doi: 10.7498/aps.42.161
[20]	LI FU-BlN. THE MICROSCOPIC PHENOMENOLOGICAL THEORY OF ANALYSIS FOR THE PROBLEM OF NONEQUILIBRIUM FLUCTUATIONS (Ⅰ)——A NEW THEORY OF EXTENDED IRREVERSIBLE THERMODY-NAMICS AND NONEQUILIBRIUM CORRECTIONS OF THE FLUCTUATION-DISSIPATION EXPRESSIONS FOR THE HEAT FL. Acta Physica Sinica, 1989, 38(9): 1467-1474. doi: 10.7498/aps.38.1467

Catalog

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

Metrics

Abstract views: 7799
PDF Downloads: 81
Cited By: 0

姓名
邮箱
手机号码
标题
留言内容
验证码

Search

Article

留言板