Maxwell's equal-area law for Gauss-Bonnet Anti-de Sitter black holes

TL;DR

This paper explores the phase transition behavior of higher-dimensional Gauss-Bonnet-AdS black holes using Maxwell's equal-area law, revealing critical phenomena similar to Van der Waals fluids, especially in specific dimensions and topologies.

Contribution

It extends the analysis of black hole phase transitions to higher dimensions and charged cases, identifying conditions for critical behavior and phase coexistence.

Findings

Critical behavior appears only in d=5 for uncharged black holes.

Charged black holes show critical behavior in d=5 and d=6 under spherical topology.

The isobar line for phase coexistence is determined using Maxwell's construction.

Abstract

Interpreting the cosmological constant \Lambda as a thermodynamic pressure and its conjugate quantity as a thermodynamic volume, we study the Maxwell's equal area law of higher dimensional Gauss-Bonnet-AdS black holes in extended phase space. These black hole solutions critically behave like Van der Waals systems. It has been realized that below the critical temperature T_c the stable equilibrium is violated. We show through calculations that the critical behaviors for the uncharged black holes only appear in d=5. For the charged case, we analyse solutions in d = 5 and d = 6 separately and find that, up to some constrains, the critical behaviors only appear in the spherical topology. Using the Maxwell's construction, we also find the isobar line for which the liquid-gas-like phases coexist.