Thermodynamics of Taub-NUT and Plebanski Solutions

TL;DR

This paper explores the thermodynamics of Taub-NUT and Plebanski solutions, revealing how NUT charge distributes along Misner strings and establishing consistent thermodynamic relations using various formalisms.

Contribution

It introduces a comprehensive method to calculate thermodynamic quantities for Taub-NUT and related solutions, accounting for Misner strings and extending the analysis to diverse black hole configurations.

Findings

NUT charge spreads along Misner strings, similar to mass in Schwarzschild.

Thermodynamic quantities satisfy the first law, Euclidean action, and Smarr relation.

Methods are extended to electric/magnetic black holes, boosted black strings, and Kaluza-Klein monopoles.

Abstract

We observe the parallel between the null Killing vector on the horizon and degenerate Killing vectors at both north and south poles in Kerr-Taub-NUT and general Plebanski solutions. This suggests a correspondence between the pairs of the angular momentum/velocity and the NUT charge/potential. We treat the time as a real line such that the Misner strings are physical. We find that the NUT charge spreads along the Misner strings, analogous to that the mass in the Schwarzschild black hole sits at its spacetime singularity. We develop procedures to calculate all the thermodynamic quantities and we find that the results are consistent with the first law (Wald formalism), the Euclidean action and the Smarr relation. We also apply the Wald formalism, the Euclidean action approach, and the (generalized) Komar integration to the electric and magnetic black holes in a class of EMD theories, and also to boosted black strings and Kaluza-Klein monopoles in five dimensions, to gain better understandings of how to deal with the subtleties associated with Dirac and Misner strings.