Hawking--Page phase transitions in four-dimensional Einstein--Gauss--Bonnet gravity

TL;DR

This paper investigates Hawking-Page phase transitions in four-dimensional Einstein-Gauss-Bonnet gravity, revealing how the GB term affects transition temperatures and conditions, with implications for charged black holes and phase behavior.

Contribution

It introduces a novel 4D Einstein-Gauss-Bonnet gravity framework and analyzes its impact on Hawking-Page phase transitions, including effects on temperature and pressure ranges.

Findings

GB term decreases HP transition temperature

HP transitions occur only within specific pressure ranges

Transition temperature decreases with electric potential in charged cases

Abstract

The Hawking-Page (HP) phase transitions of the anti-de Sitter black holes in the extended phase space are studied in a novel four-dimensional Einstein-Gauss-Bonnet (4EGB) gravity, which is proposed by rescaling the Gauss--Bonnet (GB) coupling constant $\alpha\to\alpha/(d-4)$ in $d$ dimensions and redefining the four-dimensional gravity in the limit $d \to 4$. The GB term shows nontrivial contributions to both black hole mass and entropy simultaneously, and decreases the HP phase transition temperature $T_{\rm HP}$. Moreover, the HP phase transitions can happen only within a range of pressure in the 4EGB gravity. For the charged black holes, $T_{\rm HP}$ also decreases with the electric potential in the grand canonical ensemble. A general discussion of the HP phase transitions in the Einstein, GB, and 4EGB gravities is also presented.