Journal
GENERAL RELATIVITY AND GRAVITATION
Volume 35, Issue 10, Pages 1733-1743Publisher
KLUWER ACADEMIC/PLENUM PUBL
DOI: 10.1023/A:1026058111582
Keywords
black hole; entropy; Hessian
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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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