Geometry of black hole thermodynamics

Details Geometry of black hole thermodynamics Geometry of black hole thermodynamics

2003-04-02

arxiv.org/abs/gr-qc/0304015v1

Gen.Rel.Grav.35:1733,2003

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

13 pages, 2 figures

Scientific paper

10.1023/A:1026058111582

The Hessian of the entropy function can be thought of as a metric tensor on the 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 this geometry for some families of black holes. It is flat for the BTZ and Reissner-Nordstrom black holes, while curvature singularities occur for the Reissner-Nordstrom-anti-de Sitter and Kerr black holes.

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