Critical phenomena and thermodynamic geometry of charged Gauss-Bonnet AdS black holes

TL;DR

This paper investigates the phase transitions, critical phenomena, and thermodynamic geometry of charged Gauss-Bonnet AdS black holes, revealing their dependence on cosmological constant and dimensionality, and drawing analogies with van der Waals fluids.

Contribution

It provides a detailed analysis of phase structures, critical points, and microstructure properties of charged Gauss-Bonnet AdS black holes, including the role of thermodynamic geometry.

Findings

Critical points depend on cosmological constant and dimension.

Black holes exhibit van der Waals-like phase behavior.

Ruppeiner curvature diverges at heat capacity divergence points.

Abstract

In this paper, we study the phase structure and equilibrium state space geometry of charged topological Gauss-Bonnet black holes in $d$-dimensional anti-de Sitter spacetime. Several critical points are obtained in the canonical ensemble, and the critical phenomena and critical exponents near them are examined. We find that the phase structures and critical phenomena drastically depend on the cosmological constant $\Lambda$ and dimensionality $d$. The result also shows that there exists an analogy between the black hole and the van der Waals liquid gas system. Moreover, we explore the phase transition and possible property of the microstructure using the state space geometry. It is found that the Ruppeiner curvature diverges exactly at the points where the heat capacity at constant charge of the black hole diverges. This black hole is also found to be a multiple system, i.e., it is similar to the ideal gas of fermions in some range of the parameters, while to the ideal gas of bosons in another range.