Misner Gravitational Charges and Variable String Strengths

Understand

As shown recently (arXiv:1903.08668), consistent thermodynamics of the Lorentzian Taub-NUT solutions with Misner strings present can be formulated provided a new pair of conjugate quantities (related to the NUT parameter) $\psi-N$ is introduced.

• In (arXiv:1903.08668) this pair was calculated from the Euclidean action but no geometrical interpretation for the new quantities was provided.
• In this paper we propose that the potential $\psi$ should be identified with the surface gravity of the Misner string and the conjugate Misner charge $N$ can be obtained by a Komar-type integration over the tubes surrounding the string singularities.
• We show that similar tube contributions also modify the Komar formula for the thermodynamic volume.