A conserved charge built from the nut parameter and the Misner string parameter completes the first law of Kerr-NUT thermodynamics.
The First Law for the Lorentzian Rotating Taub-NUT
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abstract
We show that the first law for the rotating Taub-NUT is straightforwardly established with the surface charge method. The entropy is explicitly found as a charge, and its value is not proportional to the horizon area. We conclude that there are unavoidable contributions from the Misner strings to the charges, still, the mass and angular momentum gets standard values. However, there are no independent charges associated with the Misner strings.
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Kerr-NUT Thermodynamics: Misner Strings and Nut Charges
A conserved charge built from the nut parameter and the Misner string parameter completes the first law of Kerr-NUT thermodynamics.