publication . Preprint . 2011

Limit of Universality of Entropy-Area Law for Multi-Horizon Spacetimes

Saida, Hiromi;
Open Access English
  • Published: 05 Sep 2011
It may be a common understanding at present that, once event horizons are in thermal equilibrium, the entropy-area law holds inevitably. However, no rigorous verification is given to such a very strong universality of the law in multi-horizon spacetimes. In this article, based on thermodynamically consistent and rigorous discussion, we investigate thermodynamics of Schwarzschild-deSitter spacetime in which the temperatures of two horizons are different. We recognize that three independent state variables exist in thermodynamics of the horizons. One of the three variables represents the effect of "external gravity" acting on one horizon due to another one. Then w...
free text keywords: General Relativity and Quantum Cosmology, High Energy Physics - Theory
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Then, because the thermal equilibrium system for BEH is the region Db, rb < r < rw, in Lorentzian SdS spacetime, we find the topology of Euclidean space of thermal equilibrium system for BEH is D2 × S2.

3 M − rb + 2 rw fw − √fw 5.4.1 where βb is the imaginary time period (5.27) and fw is in Eq.(5.30). Under the length size scaling (5.18), this temperature is scaled as Tb → λ−1 Tb. Therefore, by the assumption SdS-2, Tb is an intensive state variable of BEH.

2πrc2fw3/2 2rw 5.5.3 [5] S.W.Hawking, Particle Creation by Black Holes, Commun.Math.Phys.43 (1975) 199.

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