Thermodynamics of multi-horizon spacetimes

TL;DR

This paper investigates the thermodynamics of multi-horizon spacetimes, demonstrating the existence of a global temperature and showing that total entropy depends on horizon correlations rather than a single horizon.

Contribution

It establishes the existence of a global temperature in multi-horizon spacetimes and clarifies that total entropy is determined by horizon correlations, not just the outer horizon.

Findings

Global temperature exists in Schwarzschild-de Sitter, Reissner-Nordstrom-de Sitter, and rotating BTZ spacetimes.

The global temperature differs from the conventional Hawking temperature of the outer horizon.

Total entropy is governed by correlations between horizons, not solely by the outer horizon.

Abstract

There exist several well-established procedures for computing thermodynamics for a single horizon spacetime. However, for a spacetime with multi-horizon, the thermodynamics is not very clear. It is not fully understood whether there exists a global temperature for the multi-horizon spacetime or not. Here we show that a global temperature can exist for Schwarzschild-de Sitter spacetime, Reissner-Nordstrom-de Sitter spacetime, and rotating BTZ black hole. This temperature does not coincide with the conventional Hawking temperature related to the outer horizon. We also show that the total entropy for these spacetimes can not be determined only by the outer horizon. The correlations between the horizons of these spacetimes determine it.