RPS Thermodynamics of Taub-NUT AdS Black Holes in the Presence of Central Charge and the Weak Gravity Conjecture

Abstract

We study the thermodynamics of the Taub-NUT AdS black holes by Visser's holographic method using AdS radius as a constant parameter under the restricted phase space approach. Instead of the variables P and V , we deal with the central charge and also chemical potential as a unique couple of conjugate thermodynamic variables. We study some interesting properties of the Taub-NUT black holes e.g. supercritical phase equilibrium in the T − S processes, Q − Φ and the Hawking-Page phase transition in the µ − C processes. As a consequence, the consistency of the weak gravity conjecture of multi-charge for Taub-NUT-AdS black holes at critical points is proved. We conclude that in the presence of the central charge and assuming C = 3 8 2 , weak gravity conjecture could be satisfied in the Taub-NUT-AdS black holes with n 1.