Maxwell's equal area law for Lovelock Thermodynamics

TL;DR

This paper extends Maxwell's equal area law to Gauss-Bonnet and third order Lovelock AdS black holes in higher dimensions, analyzing phase transitions, critical points, and latent heat.

Contribution

It introduces a method to apply Maxwell's equal area law to Lovelock black holes in various dimensions, identifying phase transition points and thermodynamic properties.

Findings

Identified phase transition points for Gauss-Bonnet and Lovelock black holes.

Determined radii of black holes involved in phase transitions.

Analyzed cases with multiple critical points and latent heat.

Abstract

We present the construction of Maxwell's equal area law for the Guass-Bonnet AdS black holes in $d=5,6$ and third order Lovelock AdS black holes in $d=7,8$. The equal area law can be used to find the number and location of the points of intersection in the plots of Gibbs free energy, so that we can get the thermodynamically preferred solution which corresponds to the first order phase transition. We obtain the radius of the small and large black holes in the phase transition which share the same Gibbs free energy. The case with two critical points is explored in much more details. The latent heat is also studied.