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Flat information geometries in black hole thermodynamics. (English) Zbl 1175.83036

Summary: The Hessian of either the entropy or the energy function can be regarded as a metric on a Gibbs surface. For two parameter families of asymptotically flat black holes in arbitrary dimension one or the other of these metrics are flat, and the state space is a flat wedge. The mathematical reason for this is traced back to the scale invariance of the Einstein-Maxwell equations. The picture of state space that we obtain makes some properties such as the occurrence of divergent specific heats transparent.

MSC:

83C57 Black holes
83C22 Einstein-Maxwell equations
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