Thermodynamics and Phase Transitions of NUTty Dyons

TL;DR

This paper develops a consistent thermodynamic framework for Lorentzian Taub-NUT spacetimes with electric and magnetic charges, introducing new conjugate variables and clarifying phase transition behaviors.

Contribution

It introduces a novel thermodynamic formulation for NUTty dyons, allowing independent variation of the NUT parameter and charges without imposing Misner conditions.

Findings

NUT parameter can be varied independently in thermodynamics.

Electric and magnetic charges need not be proportional.

A full cohomogeneity first law including both charges is established.

Abstract

Picking up the threads on a recent proposal [arXiv:1903.08668], we show how to formulate consistent thermodynamics of Lorentzian Taub-NUT spacetimes in the presence of electric and magnetic charges. Namely, with an entropy identified with a quarter of the horizon area and no Misner time periodicity condition imposed, we show that a new pair of conjugate quantities can be introduced so that the NUT parameter can be independently varied and the corresponding first law and Smarr relation can be consistently formulated. Moreover, we show that (contrary to the statements in the literature) the electric and magnetic parameters need not be proportional to one another and a full cohomogeneity first law including variations of both charges can be written down, provided one charge is considered on the horizon and the other at infinity. The corresponding phase transitions are also briefly discussed.