Chin. Phys. Lett.  2017, Vol. 34 Issue (8): 080401    DOI: 10.1088/0256-307X/34/8/080401
GENERAL |
Energy and Thermodynamics of the Quantum-Corrected Schwarzschild Black Hole
Mahamat Saleh1, Bouetou Bouetou Thomas2,3,4, Timoleon Crepin Kofane3,4,5**
1Department of Physics, Higher Teachers' Training College, University of Maroua, Maroua 55, Cameroon
2Ecole Nationale Supérieure Polytechnique, University of Yaounde I, Yaounde 8390, Cameroon
3The African Center of Excellence in Information and Communication Technologies, University of Yaounde I, Yaounde 8390, Cameroon
4The Abdus Salam International Centre for Theoretical Physics, Trieste II-34014, Italy
5Department of Physics, Faculty of Science, University of Yaounde I, Yaounde 812, Cameroon
Cite this article:   
Mahamat Saleh, Bouetou Bouetou Thomas, Timoleon Crepin Kofane 2017 Chin. Phys. Lett. 34 080401
Download: PDF(488KB)   PDF(mobile)(476KB)   HTML
Export: BibTeX | EndNote | Reference Manager | ProCite | RefWorks
Abstract Energy and thermodynamics are investigated in the Schwarzschild black hole spacetime when considering corrections due to quantum vacuum fluctuations. The Einstein and Møller prescriptions are used to derive the expressions of the energy in the background. The temperature and heat capacity are also derived. The results show that due to the quantum fluctuations in the background of the Schwarzschild black hole, all the energies increase and the Einstein energy differs from Møller's one. Moreover, when increasing the quantum correction factor $a$, the difference between Einstein and Møller energies, the Unruh–Verlinde temperature as well as the heat capacity of the black hole increases while the Hawking temperature remains unchanged.
Received: 24 January 2017      Published: 22 July 2017
PACS:  04.70.Dy (Quantum aspects of black holes, evaporation, thermodynamics)  
  04.20.Jb (Exact solutions)  
  97.60.Lf (Black holes)  
TRENDMD:   
URL:  
https://cpl.iphy.ac.cn/10.1088/0256-307X/34/8/080401       OR      https://cpl.iphy.ac.cn/Y2017/V34/I8/080401
Service
E-mail this article
E-mail Alert
RSS
Articles by authors
Mahamat Saleh
Bouetou Bouetou Thomas
Timoleon Crepin Kofane
[1]Einstein A 1915 Preuss. Akad. Wiss. Berlin 47 778
[2]Papapetrou A 1948 Proc. Roy. Irish Acad. A 52 11
[3]Tolman R C 1930 Phys. Rev. 35 875
[4]Landau L D and Lifschitz E M 1951 The Classical Theory of Fields (New York: Addison-Wesley Press) chap 12 p 317
[5]Bergmann P G and Thomson R 1953 Phys. Rev. 89 400
[6]Weinberg S 1972 Gravitation and Cosmology: Principles and Applications of General Theory of Relativity (New York: John Wiley and Sons Inc.) chap 7 p 165
[7]Goldberg J N 1958 Phys. Rev. 111 315
[8]Cooperstock F I and Sarracino R S 1978 J. Phys. A 11 877
[9]Xulu S S 2007 Int. J. Theor. Phys. 46 2915
[10]Radinschi I and Grammenos T 2008 Int. J. Theor. Phys. 47 1363
[11]Vagenas E C 2006 Mod. Phys. Lett. A 21 1947
[12]Vagenas E C 2004 Mod. Phys. Lett. A 19 213
[13]Xulu S S 2003 arXiv:gr-qc/0304081v1
[14]Vagenas E C 2003 Int. J. Mod. Phys. A 18 5949
[15]Virbhadra K S 1990 Phys. Rev. D 41 1086
[16]Virbhadra K S 1990 Phys. Rev. D 42 2919
[17]Virbhadra K S 1990 Phys. Rev. D 42 1066
[18]Aguirregabiria J M, Chamorro A and Virbhadra K S 1996 Gen. Relativ. Gravitation 28 1393
[19]Xulu S S 1998 Int. J. Mod. Phys. D 7 773
[20]Radinschi I 1999 Acta Phys. Slovaca 49 789
[21]Radinschi I 2000 Fizika B 9 43
[22]Radinschi I 2000 Mod. Phys. Lett. A 15 803
[23]Xulu S S PhD Dissertation (KwaZulu-Natal: University of Zululand) 2003 arXiv:hep-th/0308070v1
[24]Mahamat S, Bouetou B T and Kofane T C 2011 Commun. Theor. Phys. 55 291
[25]Wei Y H 2008 Chin. Phys. Lett. 25 2782
[26]Wald R M 2001 Living Rev. Relativ. 4 6
[27]Carlip S 1995 Phys. Rev. D 51 632
[28]Carlip S 1997 Phys. Rev. D 55 878
[29]Strominger and Vafa 1996 Phys. Lett. B 379 99
[30]Ashtekar A, Baez J, Corichi A and Krasnov K 1998 Phys. Rev. Lett. 80 904
[31]Wang J and Huang C G 2016 Int. J. Mod. Phys. D 25 1650100
[32]Huang C G and Wang J 2016 Gen. Relativ. Gravit. 48 115
[33]Huang C G, Liu L and Zhao Z 1993 Gen. Relativ. Gravit. 25 1267
[34]Hawking S W 1975 Commun. Math. Phys. 43 199
[35]Hawking S W 1884 Nature 30 248
[36]Bekenstein J D 1973 Phys. Rev. D 7 2333
[37]Pete M 2009 arXiv:physics.pop-ph/0906.4849v1
[38]Farmanya A, Abbasi S and Naghipour A 2008 Acta Phys. Pol. A 114 651
[39]Zhao R, Zhao H X and Hu S Q 2007 Mod. Phys. Lett. A 22 1737
[40]Gibbons G W and Hawking S W 1977 Phys. Rev. D 15 2738
[41]Parikh M K and Wilczek F 1998 Phys. Rev. D 58 064011
[42]Bardeen J M, Carter B and Hawking S W 1973 Commun. Math. Phys. 31 161
[43]Mahamat S, Bouetou B T and Kofane T C 2012 Gen. Relativ. Gravit. 44 2181
[44]Mathur S D 2009 Class. Quantum Grav. 26 224001
[45]Sharif M and Javed W 2012 Astrophys. Space Sci. 337 335
[46]Wontae K and Yongwan K 2012 Phys. Lett. B 718 687
[47]Mahamat S, Bouetou B T and Kofane T C 2014 Astrophys. Space Sci. 350 721
[48]Mahamat S, Bouetou B T and Kofane T C 2016 Astrophys. Space Sci. 361 137
[49]Kazakov D I and Solodukhin S N 1994 Nucl. Phys. B 429 153
[50]Yang C and Radinschi I 2004 Chin. J. Phys. 42 40
[51]Verlinde E 2011 J. High Energy Phys. 1104 029
[52]Unruh W G 1976 Phys. Rev. D 14 870
[53]Konoplya R A 2010 Eur. Phys. J. C 69 555
[54]Liu Y X, Wang Y Q and Wei S W 2010 Class. Quantum Grav. 27 185002
[55]Han Y and Lan M 2011 Int. J. Theor. Phys. 50 899
Related articles from Frontiers Journals
[1] Qian Dong, M. A. Mercado Sanchez, Guo-Hua Sun, Mohamad Toutounji, Shi-Hai Dong. Tripartite Entanglement Measures of Generalized GHZ State in Uniform Acceleration[J]. Chin. Phys. Lett., 2019, 36(10): 080401
[2] Chi-Kun Ding. Gravitational Perturbations in Einstein Aether Black Hole Spacetime[J]. Chin. Phys. Lett., 2018, 35(10): 080401
[3] Chang-Qing Liu, Chi-Kun Ding, Ji-Liang Jing. Effects of Homogeneous Plasma on Strong Gravitational Lensing of Kerr Black Holes[J]. Chin. Phys. Lett., 2017, 34(9): 080401
[4] Jun Liang. The $P$–$v$ Criticality of a Noncommutative Geometry-Inspired Schwarzschild-AdS Black Hole[J]. Chin. Phys. Lett., 2017, 34(8): 080401
[5] M. Azam, A. Aslam. Accretion onto the Magnetically Charged Regular Black Hole[J]. Chin. Phys. Lett., 2017, 34(7): 080401
[6] Xiao-Xiong Zeng, Xin-Yun Hu, Li-Fang Li. Effect of Phantom Dark Energy on Holographic Thermalization[J]. Chin. Phys. Lett., 2017, 34(1): 080401
[7] Jun-Jin Peng, Wen-Chang Xiang, Shao-Hong Cai. Abbott–Deser–Tekin Charge of Dilaton Black Holes with Squashed Horizons[J]. Chin. Phys. Lett., 2016, 33(08): 080401
[8] Belhaj A., Chabab M., El Moumni H., Masmar K., Sedra M. B.. On Hawking Radiation of 3D Rotating Hairy Black Holes[J]. Chin. Phys. Lett., 2015, 32(10): 080401
[9] MA Meng-Sen, ZHAO Ren. Notes on Phase Transition of Nonsingular Black Hole[J]. Chin. Phys. Lett., 2015, 32(03): 080401
[10] ZHANG Ming, YUE Rui-Hong, YANG Zhan-Ying. Critical Behavior of Black Holes in an Einstein–Maxwell Gravity with a Conformal Anomaly[J]. Chin. Phys. Lett., 2015, 32(02): 080401
[11] LAI Chu-Yu, CHEN Ju-Hua, WANG Yong-Jiu. The Motion of Spinning Particles in the Spacetime of a Black Hole with a Cosmic String Topological Defect[J]. Chin. Phys. Lett., 2014, 31(09): 080401
[12] HE Tang-Mei, YANG Jin-Bo, ZHANG Jing-Yi. Corrected Stefan–Boltzmann Law and Lifespan of a Black Hole[J]. Chin. Phys. Lett., 2014, 31(08): 080401
[13] Ahmad Sheykhi. Quasi-Topological Cosmology from Emergence of Cosmic Space[J]. Chin. Phys. Lett., 2014, 31(2): 080401
[14] FANG Heng-Zhong, ZHOU Kai-Hu. Emission of Phonons from a Rotating Sonic Black Hole[J]. Chin. Phys. Lett., 2014, 31(1): 080401
[15] G. Abbas, R. M. Ramzan. Thermodynamics of Phantom Energy Accreting onto a Black Hole in Einstein–Power–Maxwell Gravity[J]. Chin. Phys. Lett., 2013, 30(10): 080401
Viewed
Full text


Abstract