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

TL;DR

This paper rigorously examines the universality of the entropy-area law in multi-horizon spacetimes, revealing conditions under which the law breaks down, especially in Schwarzschild-de Sitter spacetime with unequal horizon temperatures.

Contribution

It introduces a thermodynamic framework with three independent variables, demonstrating the potential breakdown of the entropy-area law in multi-horizon spacetimes.

Findings

Entropy-area law can break down in multi-horizon spacetimes with different horizon temperatures.

Three independent thermodynamic variables are necessary to describe such systems.

The cosmological constant plays a special role in horizon thermodynamics.

Abstract

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 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.