Ehrenfest scheme for $P-V$ criticality of higher dimensional charged black holes, rotating black holes and Gauss-Bonnet AdS black holes

Understand

To provide an analytic verification of the nature of phase transition at the critical point of $P-V$ criticality, the original expressions of Ehrenfest equations have been introduced directly.

• By treating the cosmological constant and its conjugate quantity as thermodynamic pressure and volume respectively, we carry out analytical check of classical Ehrenfest equations.
• To show that our approach is universal, we investigate not only higher-dimensional charged AdS black holes, but also rotating AdS black holes.
• Not only are the examples of Einstein gravity shown, but also the example of modified gravity is presented for Gauss-Bonnet AdS black holes.