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Ruppeiner Geometry of Black Hole Thermodynamics

Published online by Cambridge University Press:  30 September 2008

A. Oscoz ,
E. Mediavilla ,
M. Serra-Ricart ,
J.E. Åman  and
N. Pidokrajt
J.E. Åman*
Affiliation:
Department of Physics, Stockholm University, Sweden
N. Pidokrajt
Affiliation:
Department of Physics, Stockholm University, Sweden
*
[email protected]
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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.

Type
Research Article
Information
European Astronomical Society Publications Series , Volume 30: Spanish Relativity Meeting - Encuentros Relativistas Españoles , ERE2007: Relativistic Astrophysics and Cosmology , 2008 , pp. 269 - 273
Copyright
© EAS, EDP Sciences, 2008

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References

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