Ruppeiner Geometry of Black Hole Thermodynamics
arXiv:0801.0016 · doi:10.1051/eas:0830042
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.
5 pages, 2 figures. Talk given at 30th Spanish Relativity Meeting (ERE 2007): Relativistic Astrophysics And Cosmology, 10-14 Sep 2007, Puerto de La Cruz, Tenerife, Spain