Phase transition of the higher dimensional charged Gauss-Bonnet black hole in de Sitter spacetime

TL;DR

This paper investigates the phase transition behavior of charged Gauss-Bonnet black holes in de Sitter spacetime, revealing a second-order phase transition characterized by effective thermodynamic quantities and critical points influenced by the Gauss-Bonnet parameter.

Contribution

It introduces an effective temperature approach to analyze the thermodynamics of charged Gauss-Bonnet-de Sitter black holes, identifying second-order phase transitions and the impact of the Gauss-Bonnet parameter.

Findings

Black holes exhibit a second-order phase transition at the critical point.

Effective temperature and pressure decrease as the Gauss-Bonnet parameter increases.

Thermodynamic quantities satisfy the first law on both horizons with additional interconnections.

Abstract

We study the phase transition of charged Gauss-Bonnet-de Sitter (GB-dS) black hole. For black holes in de Sitter spacetime, there is not only black hole horizon, but also the cosmological horizon. The thermodynamic quantities on the both horizons satisfy the first law of the black hole thermodynamics, respectively; moreover, there are additional connections between them. Using the effective temperature approach, we obtained the effective thermodynamic quantities of charged GB-dS black hole. According to Ehrenfest classification, we calculate some response functions and plot their figures, from which one can see that the spacetime undergoes a second-order phase transition at the critical point. It is shown that the critical values of effective temperature and pressure decrease with the increase of the value of GB parameter $\alpha$.