Critical behavior of Gauss-Bonnet black holes via an alternative phase space

Understand

Recently, it was argued that charged Anti-de Sitter (AdS) black holes admit critical behavior, without extending phase space, similar to the Van der Waals fluid system in the $Q^2-\Psi$ plans where $\Psi=1/v$ (the conjugate of $Q^2$) is the inverse of the specific volume \cite{Dehy}.

• In this picture, the square of the charge of the black hole, $Q^2$, is treated as a thermodynamic variable and the cosmological constant $\Lambda$ is fixed.
• In this paper, we would like to examine whether this new approach toward critical behaviour of AdS black holes can work in other gravity such as Gauss-Bonnet (GB) gravity as well as in higher dimensional spacetime.
• We obtain the equation of state, $Q^2=Q^2(\Psi, T)$, Gibbs free energy and the critical quantities of the system, and study the effects of the GB coupling $\tilde{\alpha}$ on their behaviour.