# The Hawking-Page phase transitions in the extended phase space in the Gauss-Bonnet gravity

## TL;DR

This paper investigates Hawking-Page phase transitions in Gauss-Bonnet gravity within extended phase space, analyzing how the Gauss-Bonnet term influences phase structures, transition temperatures, and free energies for various black holes.

## Contribution

It systematically studies the effects of the Gauss-Bonnet term on phase transitions in extended phase space for different black hole configurations, combining analytical and numerical approaches.

## Key findings

- Phase transition temperature decreases with electric potential and angular velocity.
- Gauss-Bonnet coupling constant reduces the Hawking-Page transition temperature.
- Terminal points exist in the coexistence lines of phase transitions.

## Abstract

In this paper, the Hawking-Page phase transitions between the black holes and thermal anti-de Sitter (AdS) space are studied with the Gauss-Bonnet term in the extended phase space, in which the varying cosmological constant plays the role of an effective thermodynamic pressure. The Gauss-Bonnet term exhibits its effects via introducing the corrections to the black hole entropy and Gibbs free energy. The global phase structures, especially the phase transition temperature $T_{\rm HP}$ and the Gibbs free energy $G$, are systematically investigated, first for the Schwarzschild-AdS black holes and then for the charged and rotating AdS black holes in the grand canonical ensembles, with both analytical and numerical methods. It is found that there are terminal points in the coexistence lines, and $T_{\rm HP}$ decreases at large electric potentials and angular velocities and also decreases with the Gauss-Bonnet coupling constant $\alpha$.