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

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 $T_{\mathrm{HP}}$. Moreover, the HP phase transitions can happen only within a range of pressure in the 4EGB gravity. For the charged black holes, $T_{\mathrm{HP}}$ 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.

12 pages, 11 figures, Physics of the Dark Universe 31 (2021) 100769