A Commentary on Ruppeiner Metrics for Black Holes

Abstract

There has been some recent controversy regarding the Ruppeiner metrics that are induced by Reissner-Nordstrom (and Reissner-Nordstrom-like) black holes. Most infamously, why does this family of metrics turn out to be flat, how is this outcome to be physically understood, and can/should the formalism be suitably modified to induce curvature? In the current paper, we provide a novel interpretation of this debate. For the sake of maximal analytic clarity and tractability, some supporting calculations are carried out for the relatively simple model of a rotating BTZ black hole.

15 pages; v2, typos corrected and a few references added

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• Hessian matrix, specific heats, Nambu brackets, and thermodynamic geometry
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• Geometrothermodynamics of higher dimensional black holes
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• Geometrothermodynamics in Horava-Lifshitz gravity
• Thermodynamic Metrics and Black Hole Physics
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