The extended thermodynamic properties of a topological Taub–NUT/Bolt–AdS spaces

We consider higher dimensional topological Taub–NUT/Bolt–AdS solutions where a cosmological constant is treated as a pressure. The thermodynamic quantities of these solutions are explicitly calculated. Furthermore, we find these thermodynamic quantities satisfying the Clapeyron equation. In particular, a new thermodynamically stable region for the NUT solution is found by studying the Gibbs free energy. Intriguingly, we also find that like the AdS black hole case, the G−TG−T diagram of the Bolt solution has two branches which are joined at a minimum temperature. The Bolt solution with the large radius, at the lower branch, becomes stable beyond a certain temperature while the Bolt solution with the small radius, at the upper branch, is always unstable.