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

摘要

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 chapter, based on thermodynamically consistent and rigorous discussion, we investigate thermodynamics of Schwarzschild-de Sitter 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 we find that thermodynamic formalism with three independent variables suggests the breakdown of entropy-area law, and clarifies the necessary and sufficient condition for the entropy-area law. As a by-product, the special role of cosmological constant in thermodynamics of horizons is also revealed. Finally we propose two discussions; one of them is on the quantum statistics of underlying quantum gravity, and another is on the Schwarzschild-de Sitter black hole evaporation from the point of view of non-equilibrium thermodynamics.