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Revista mexicana de física
versión impresa ISSN 0035-001X
Rev. mex. fis. vol.60 no.1 México feb. 2014
Investigación
Thermodynamic response functions and Maxwell relations for a Kerr black hole
L. Escamilla and J. Torres-Arenas
División de Ciencias e Ingenierías Campus León, Universidad de Guanajuato, Loma del Bosque 103, 37150 León Guanajuato, México, e-mail: lescamilla@fisica.ugto.mx; jtorres@fisica.ugto.mx
Received 18 February 2013.
Accepted 4 October 2013.
Abstract
Assuming the existence of a fundamental thermodynamic relation, the classical thermodynamics of a black hole with mass and angular momentum is given. New definitions of the response functions and TdS equations are introduced and mathematical analogous of the Euler equation and Gibbs-Duhem relation are founded. Thermodynamic stability is studied from concavity conditions, resulting in an unstable equilibrium at all the domain except for a region of local stable equilibrium. The Maxwell relations are written, allowing to build the thermodynamic squares. Our results shown an interesting analogy between thermodynamics of gravitational and magnetic systems.
Keywords: Thermodynamics; black holes; long range interactions.
PACS: 05.70.-a; 04.70.Bw; 95.30.Tg
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Acknowledgments
We want to acknoweledge CONACyT (proyect-152684) and the University of Guanajuato (DAIP-006/10) for the support in the realization of this work.
References
1. H.B. Callen, Thermodynamics and an Introduction to Thermo-statistics, 2nd ed. (John Willey & Sons, Singapore, 1985) pp. 35, 183. [ Links ]
2. W. Greiner, L. Neise and H. Stoker, Thermodynamics and Statistical Mechanics, 1st ed. (Springer-Verlag, NY, 1995) pp. 4, 218. [ Links ]
3. T. Dauxois, S. Ruffo, et. al. (editors), Dynamics and thermodynamics of systems with long range interactions: an introduction, (Lect. Notes in Phys. vol 602), 1st ed. (Springer, Berlin, 2002). [ Links ]
4. R.S. Johal, A. Planes and E. Vives, Preprint cond-mat/0503329 (2005). [ Links ]
5. A. Campa, T. Dauxois and S. Ruffo, Phys. Rep. 480 (2009) 57. [ Links ]
6. J.D. Bekenstein, Phys. Rev. D 7 (1973) 2333. [ Links ]
7. J.D. Bekenstein, Phys. Rev. D 12 (1975) 3077. [ Links ]
8. J.M. Baerdeen, B. Carter and S.W. Hawking, Commun. Math. Phys. 31 (1973) 161. [ Links ]
9. P. Candelas and D.W. Sciama, Phys. Rev. Lett. 38 (1977) 1372. [ Links ]
10. P.C.W. Davies, Rep. Prog. Phys. 41 (1978) 1313. [ Links ]
11. R.M. Wald, Liv. Rev. Rel. 4 (2001) 6. [ Links ]
12. E.A. Martinez, Phys. Rev. D 53 (1996) 7062. [ Links ]
13. E.A. Martinez, Phys. Rev. D 54 (1996) 6302. [ Links ]
14. P.S. Custodio and J.E. Horvath, Am. J. Phys. 71 (2003) 1237. [ Links ]
15. J.W. York Jr, Phys. Rev. D 33 (1986) 2092. [ Links ]
16. H.W. Braden, J.D. Brown, B.F. Whiting and J.W. York Jr, Phys. Rev. D 42 (1990) 3376. [ Links ]
17. J.D. Brown, J. Creighton and R.B. Mann, Phys. Rev. D 50 (1994) 6394. [ Links ]
18. C. Peca and J.P.S. Lemos, Phys. Rev. D 59 (1999) 124007. [ Links ]
19. M.M. Akbar, Phys. Rev. D 82 (2010) 064001. [ Links ]
20. R. D'Inverno, Introducing Einstein's Relativity, 1sted. (Oxford University Press, NY, 1992) pp. 248. [ Links ]
21. S.W. Hawking, Phys. Rev. D 13 (1976) 191. [ Links ]
22. J.D. Bekenstein, Physics Today (Jan 1980) 24. [ Links ]
23. C.W. Misner, K. S. Thorne and J.A. Wheeler, Gravitation (W.H. Freeman, SF, 1973), pp. 878, 907. [ Links ]
24. T. Padmanabhan, Phys. Rev. 188 (1990) 285. [ Links ]
25. J. Oppenheim, Phys. Rev. E 68 (2003) 016108. [ Links ]
26. B.R. Parker and R.J. McLeod, Am. J. Phys. 48 (1989) 1066. [ Links ]
27. M.-H. Phan and S.-C. Y, J. Magn. Magn. Mater. 308 (2007) 325. [ Links ]
28. P.C.W. Davies, Class. Quantum Grav. 6 (1989) 1909. [ Links ]
29. F.O. Koenig, J. Chem. Phys. 3 (1935) 29. [ Links ]
30. H.E. Stanley, Introduction to Phase Transitions and Critical Phenomena, 1st ed. (Oxford University Press, London, 1971), pp. 34. [ Links ]