Ruppeiner Geometry of Black Hole Thermodynamics

Details Ruppeiner Geometry of Black Hole Thermodynamics Ruppeiner Geometry of Black Hole Thermodynamics

2007-12-28

arxiv.org/abs/0801.0016v1

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

5 pages, 2 figures. Talk given at 30th Spanish Relativity Meeting (ERE 2007): Relativistic Astrophysics And Cosmology, 10-14 S

Scientific paper

10.1051/eas:0830042

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--Nordstr\"om 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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