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, $$Q-\Phi $$ and the Hawking-Page phase transition in the $$\mu -C$$ 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 $$C=\frac{3}{8}\ell ^2$$ , weak gravity conjecture could be satisfied in the Taub–NUT-AdS black holes with $${\hat{n}}\ll 1$$ .