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 T HP . Moreover, the HP phase transitions can occur only within a range of pressure in the 4EGB gravity. For the charged black holes, T 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.