A note on the calculation of the Komar integral in the Lorentzian Taub-NUT spacetime

TL;DR

This paper examines the calculation of the Komar integral in Lorentzian Taub-NUT spacetime, demonstrating consistent thermodynamic expressions whether Misner-string singularities are included or removed, highlighting hypersurface dependence.

Contribution

It shows how to obtain consistent thermodynamic results in Lorentzian Taub-NUT spacetime regardless of the presence of Misner-string singularities, clarifying hypersurface dependence.

Findings

Consistent thermodynamic expressions are derived with Misner-string singularities.

Removing Misner strings via Misner's procedure still requires careful hypersurface choice.

Different hypersurfaces can lead to different physical interpretations.

Abstract

It has recently been shown that one can derive consistent thermodynamical expressions in the Lorentzian Taub--NUT spacetime keeping the Misner-string singularities and taking into account their contributions in the Komar integrals. We show how the same results are obtained when the Mister-string singularities are removed by using Misner's procedure because, even though the complete spacetime has no such singularities anymore, they are unavoidable in all spacelike hypersurfaces which are used in the Komar integrals. Different choices of hypersurfaces may contain different strings and lead to different physics, though.