Triple points and phase diagrams in the extended phase space of charged Gauss-Bonnet black holes in AdS space

Abstract

We study the triple points and phase diagrams in the extended phase space of the charged Gauss-Bonnet black holes in $d$-dimensional anti-de Sitter space, where the cosmological constant appears as a dynamical pressure of the system and its conjugate quantity is the thermodynamic volume of the black holes. Employing the equation of state $T=T(v, P)$, we demonstrate that the information of the phase transition and behavior of the Gibbs free energy are potential encoded in the $T-v$ ($T-r_{h}$) line with fixed pressure $P$. We get the phase diagrams for the charged Gauss-Bonnet black holes with different values of the charge $Q$ and dimension $d$. The result shows that the small/large black hole phase transitions appear for any $d$, which is reminiscent of the liquid/gas transition of a van der Waals type. Moreover, the interesting thermodynamic phenomena, i.e., the triple points and the small/intermediate/large black hole phase transitions are observed for $d=6$ and $Q\in(0.1705, 0.1946)$.