The application of the Unruh procedure to the Rindler approximation of the Kerr-Newman metric in the neighborhood of the event and Cauchy horizons leads, unambiguously, to the well-known positive Hawking (black hole) temperature at the outer horizon, but to a negative (white hole) temperature at the inner horizon. Some consequences for the heat capacities and the status of the third law of thermodynamics are also discussed.
References
[1]
Rindler, W. (1966) Kruskal Space and the Uniformly Accelerated Frame. American Journal of Physics, 34, 1174-1178. https://doi.org/10.1119/1.1972547
[2]
Newman, E.T., Couch, E., Chinnapared, K., Exton, A., Prakash, A. and Torrence, R. (1965) Metric of a Rotating, Charged Mass. Journal of Mathematical Physics, 6, 918-919. https://doi.org/10.1063/1.1704351
[3]
Unruh, W.G. (1976) Notes on Black Hole Evaporation. Physical Review D, 14, 870-892. https://doi.org/10.1103/PhysRevD.14.870
[4]
Camargo, H.A. and Socolovsky, M. (2015) Rindler Approximation to Kerr-Newman Black Hole. The European Physical Journal Plus, 130, Article No. 230. https://doi.org/10.1140/epjp/i2015-15230-2
[5]
Wu, S.Q. and Cai, X. (2000) Generalized Laws of Black Hole Thermodynamics and Quantum Conservation Laws on Hawking Radiation Process. Il Nuovo Cimento B, 115, 143-150.
[6]
Liu, B. and Liu, W.-B. (2010) Negative Temperature of Inner Horizon and Planck Absolute Entropy of a Kerr-Newman Black Hole. Communications in Theoretical Physics (Beijing, China), 53, 83-86. https://doi.org/10.1088/0253-6102/53/1/19
[7]
Okamoto, I. and Kaburaki, O. (1992) The Inner-Horizon Thermodynamics of Kerr Black Holes. Monthly Notices of the Royal Astronomical Society, 255, 539-544. https://doi.org/10.1093/mnras/255.3.539
[8]
Cvetic, M., Gibbons, G.W., L, H. and Pope, C.N. (2018) Negative Temperatures and Entropy Super-Additivity. Physical Review D, 98, Article ID: 106015. https://doi.org/10.1103/PhysRevD.98.106015
[9]
Ramsey, N.F. (1956) Thermodynamics and Statistical Mechanics at Negative Absolute Temperatures. The Physical Review, 103, 20-28. https://doi.org/10.1103/PhysRev.103.20
Purcell, E.M. and Pound, R.V. (1951) A Nuclear Spin System at Negative Temperature. The Physical Review, 81, 279-280. https://doi.org/10.1103/PhysRev.81.279
[12]
Abragam, A. and Proctor, W.G. (1958) Spin Temperature. The Physical Review, 109, 1441-1458. https://doi.org/10.1103/PhysRev.109.1441
[13]
Baldovin, M., Iubini, S., Livi, R. and Vulpiani, A. (2021) Statistical Mechanics of Systems with Negative Temperature. Physics Reports, 923, 1-50. https://doi.org/10.1016/j.physrep.2021.03.007
[14]
Lee, T.D. (1986) Are Black Holes Blackbodies? Nuclear Physics B, 264, 437-486. https://doi.org/10.1016/0550-3213(86)90493-1
[15]
Hawking, S.W. (1975) Particle Creation by Black Holes. Communications in Mathematical Physics, 43, 199-220. Erratum: Communications in Mathematical Physics, 46, 206 (1976). https://doi.org/10.1007/BF02345020
[16]
Wald, R.M. (1997) “Nernst Theorem” and Black Hole Thermodynamics. Physical Review D, 56, 6467-6474. https://doi.org/10.1103/PhysRevD.56.6467
[17]
Davies, P.C.W. (1977) The Thermodynamic Theory of Black Holes. Proceedings of the Royal Society of London. Series A, 353, 499-521. https://doi.org/10.1098/rspa.1977.0047
[18]
Belgiorno, F. and Martellini, M. (2004) Black Holes and the Third Law of Thermodynamics. International Journal of Modern Physics D, 13, 739-770. https://doi.org/10.1142/S0218271804004876
[19]
Wreszinski, W.F. and Abdalla, E. (2009) A Precise Formulation of the Third Law of Thermodynamics. Journal of Statistical Physics, 134, 781-792. https://doi.org/10.1007/s10955-009-9693-5
[20]
Lüst, D. and Vleeshouwers, W. (2019) Black Hole Information and Thermodynamics. Springer, Berlin, 47. https://doi.org/10.1007/978-3-030-10919-6
[21]
Witten, E. (2020) Light Rays, Singularities, and All That. Reviews of Modern Physics, 92, Article ID: 045004. https://doi.org/10.1103/RevModPhys.92.045004
