Thermodynamical multihair and phase transitions of 4-dimensional charged Taub-NUT-AdS spacetimes

TL;DR

This paper investigates how the NUT parameter influences phase transitions in four-dimensional charged Taub-NUT-AdS spacetimes, revealing bounds on the parameter and its effects on the analogy to van der Waals transitions.

Contribution

It introduces the thermodynamic multihair interpretation of the NUT parameter and analyzes its impact on phase transition behavior in these spacetimes.

Findings

Existence of an upper bound on the NUT parameter for critical points.

Small NUT parameter preserves van der Waals analogy.

Large NUT parameter leads to different phase transition types.

Abstract

We study the behavior of phase transitions for the four-dimensional charged Taub-NUT-AdS spacetime with the Newman-Unti-Tamburino (NUT) parameter interpreted as the thermodynamic multihair in the extended thermodynamic phase space, and mainly focus on the effects of the NUT parameter on the phase transitions. We find that there is an upper bound on the value of the NUT parameter beyond which the corresponding physical inflection point or critical point will not exist, and the thermodynamic trihair interpretation of the NUT parameter would admit a little larger upper bound than the thermodynamic bihair interpretation. Moreover, as long as the NUT parameter is vanishingly small, the analogy to the van der Waals liquid/gas phase transition is valid irrespective of the multihair characteristics of the NUT parameter. However, as the NUT parameter increases to be comparable to the electric charge, such analogy to the van der Waals system will be broken, and the corresponding inflection point is not a thermodynamic critical point any more. For a large NUT parameter, there are frequent occurrences of the zeroth order phase transition in the case of the thermodynamic bihair interpretation, while only the first order phase transition happens in the case of the thermodynamic trihair interpretation.