Ruppeiner Geometry of RN Black Holes: Flat or Curved?

Abstract

In some recent studies \cite{aman1, aman2, aman3}, Aman {\it et al.} used the Ruppeiner scalar as a measure of underlying interactions of Reissner-Nordström black holes, indicating that it is a non-interacting statistical system for which classical thermodynamics could be used at any scale. Here, we show that if we use the complete set of thermodynamic variables, a non-flat state space will be produced. Furthermore, the Ruppeiner curvature diverges at extremal limits, as it would for other types of black holes.

9 pages

References in corpus (3)

• Thermodynamic Geometry and Critical Behavior of Black Holes
• On the Thermodynamic Geometry of BTZ Black Holes
• Flat Information Geometries in Black Hole Thermodynamics

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