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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 metrictensor on state space. In the context of thermodynamicalfluctuation theory Ruppeiner has argued that the Riemannian geometryof this metric gives insight into the underlying statisticalmechanical system; the claim is supported by numerous examples. Westudy these geometries for some families of black holes and find thatthe Ruppeiner geometry is flat for Reissner–Nordström black holesin any dimension, while curvature singularities occur for the Kerrblack 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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