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arXiv · hep-th/0703030

The Disjointed Thermodynamics of Rotating Black Holes With a NUT Twist

A. M. Ghezelbash·R. B. Mann·Rafael D. Sorkin
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Abstract

We study the solutions of the Euclidean-signature Einstein equations (gravitational instantons) whose line-element takes the Kerr-bolt form, characterized by three real parameters: a size, a NUT charge, and a spin rate. The exclusion of singularities eliminates most combinations of these parameters, leaving only separated solution-manifolds between which continuous transitions are impossible (The angular velocity divided by the temperature is forced to be a rational multiple of $2π$). This ``quantization'' prevents the free variations presupposed by an equation like $T dS=dM + ΩdJ$, and thereby renders the first law true, false, meaningless, or tautological, depending on how one approaches it.

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A. M. Ghezelbash, R. B. Mann, Rafael D. Sorkin. 2007-03-04. The Disjointed Thermodynamics of Rotating Black Holes With a NUT Twist. https://doi.org/10.1016/j.nuclphysb.2007.04.004

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