Extended thermodynamics of Taub-NUT and Einstein-scalar spacetimes

Abstract

The main objective of this thesis is to summarize recent developments on the thermodynamics of both AdS Einstein-scalar spacetimes and Lorentzian Taub-NUT spacetimes. We summarize and apply well-known techniques in black hole thermodynamics to derive the extended first law of hairy AdS black holes. In particular, we provide expressions for the thermodynamic volume. For solutions in which the scalar field decays quickly enough, we find a relation between this volume and the integral of the potential behind the horizon. In a more general case, we show that the thermodynamic volume acquires additional terms proportional to the trace of the holographic stress tensor. We speculate that this result holds in even greater generality since previous evidence suggests that the same terms appear in spacetimes with non-AdS boundary conditions.

We also study the extended thermodynamics of Lorentzian Taub-NUTs in the presence of a Misner string. We review why these spacetimes are not necessarily pathological, meaning that it is reasonable to study their thermodynamics. Introducing a new charge and potential allows us to establish a consistent first law of thermodynamics for the Taub-NUT-AdS spacetime when the horizon and the NUT charge are allowed to vary independently. Additionally, we give a geometric prescription to calculate the thermodynamic charges and potentials. We then extend this first law to AdS NUTty dyons, flat Kerr-NUT, and a novel non-linear theory of electrodynamics. We propose different physical interpretations for the new terms introduced in the first law and pave the way for future research in this area.