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-Nordstr\"{o}m 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.