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 − 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 nˆ 1.
