Thermodynamics of Schwarzschild-de Sitter black hole: thermal stability of Nariai black hole

TL;DR

This paper investigates the thermodynamic stability of five-dimensional Schwarzschild-de Sitter black holes, finding that the Nariai black hole is unstable under certain temperature normalizations, with implications for black hole thermodynamics.

Contribution

It introduces two temperature normalizations for analyzing black hole thermodynamics and compares their implications for the stability of Nariai black holes.

Findings

Nariai black hole is thermodynamically unstable.

Standard normalization favors thermodynamic stability.

Bousso-Hawking normalization does not favor stability.

Abstract

We study thermodynamics of the Schwarzschild-de Sitter black hole in five dimensions by introducing two temperatures based on the standard and Bousso-Hawking normalizations. We use the first-law of thermodynamics to derive thermodynamic quantities. The two temperatures indicate that the Nariai black hole is thermodynamically unstable. However, it seems that black hole thermodynamics favors the standard normalization, and does not favor the Bousso-Hawking normalization.