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arXiv · 0801.0016

Ruppeiner Geometry of Black Hole Thermodynamics

Jan E. Aman·Narit Pidokrajt
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Abstract

The Hessian of the entropy function can be thought of as a metric tensor on state space. In the context of thermodynamical fluctuation theory Ruppeiner has argued that the Riemannian geometry of this metric gives insight into the underlying statistical mechanical system; the claim is supported by numerous examples. We study these geometries for some families of black holes and find that the Ruppeiner geometry is flat for Reissner--Nordström black holes in any dimension, while curvature singularities occur for the Kerr black holes. Kerr black holes have instead flat Weinhold curvature.

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Jan E. Aman, Narit Pidokrajt. 2007-12-28. Ruppeiner Geometry of Black Hole Thermodynamics. https://doi.org/10.1051/eas%3A0830042

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