Thermodynamic properties of black holes in de Sitter space

TL;DR

This paper investigates the thermodynamic behavior of Schwarzschild-de Sitter and Reissner-Nordström-de Sitter black holes, deriving effective thermodynamic quantities and analyzing their stability and phase transitions.

Contribution

It introduces a method to derive effective thermodynamic quantities for de Sitter black holes that satisfy Smarr-like relations, including in the Nariai limit.

Findings

Effective temperatures remain nonzero in the Nariai limit.

Schwarzschild-de Sitter black holes are thermodynamically stable.

Reissner-Nordström-de Sitter black holes can undergo phase transitions.

Abstract

We study the thermodynamic properties of Schwarzschild-de Sitter (SdS) black hole and Reissner-Nordstr\"{o}m-de Sitter (RNdS) black hole in the view of global and effective thermodynamic quantities. Making use of the effective first law of thermodynamics, we can derive the effective thermodynamic quantities of de Sitter black holes. It is found that these effective thermodynamic quantities also satisfy Smarr-like formula. Especially, the effective temperatures are nonzero in the Nariai limit, which is consistent with the idea of Bousso and Hawking. By calculating heat capacity and Gibbs free energy, we find SdS black hole is always thermodynamically stable and RNdS black hole may undergoes phase transition at some points.