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Kerr–Newman black hole thermodynamical state space: blockwise coordinates

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Abstract

A coordinate system that blockwise-simplifies the Kerr–Newman black hole’s thermodynamical state space Ruppeiner metric geometry is constructed, with discussion of the limiting cases corresponding to simpler black holes. It is deduced that one of the three conformal Killing vectors of the Reissner–Nordström and Kerr cases (whose thermodynamical state space metrics are 2 by 2 and conformally flat) survives generalization to the Kerr–Newman case’s 3 by 3 thermodynamical state space metric.

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Acknowledgments

I thank Ingemar Bengtsson for pointing out the alignment in point 2.4 of the Discussion, albeit in the context that my blockwise minimal expression for the Ruppeiner thermodynamic state space metric for the Kerr–Newman black hole did not possess it. It was down to me to point out that, on the other hand the Legendre transformation invariant thermodynamic state space metric for the Kerr–Newman black hole does possess this alignment, which could be helpful in the study of this other state space metric metric. I also thank Narit Pidokrajt, Malcolm MacCallum and the anonymous referees for various discussions and points. I acknowledge Grant FQXi-RFP3-1101 from the Foundational Questions Institute (FQXi) Fund, administered by Silicon Valley Community Foundation, Theiss Research and the CNRS, hosted with Marc Lachieze-Rey at APC. Finally, this work was started whilst at Peterhouse and DAMTP, Cambridge, so I also acknowledge a Peterhouse Research Fellowship.

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  1. DAMTP, Cambridge, UK

    Edward Anderson

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  1. Edward Anderson
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Anderson, E. Kerr–Newman black hole thermodynamical state space: blockwise coordinates. Gen Relativ Gravit 45, 2545–2551 (2013). https://doi.org/10.1007/s10714-013-1603-0

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