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 α→α∕(d−4) in d dimensions and redefining the four-dimensional gravity in the limit d→4. The GB term shows nontrivial contributions to both black hole mass and entropy simultaneously, and decreases the HP phase transition temperature THP. Moreover, the HP phase transitions can occur only within a range of pressure in the 4EGB gravity. For the charged black holes, THP 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.