Unified geometric description of black hole thermodynamics

Understand

In the space of thermodynamic equilibrium states we introduce a Legendre invariant metric which contains all the information about the thermodynamics of black holes.

• The curvature of this thermodynamic metric becomes singular at those points where, according to the analysis of the heat capacities, phase transitions occur.
• This result is valid for the Kerr-Newman black hole and all its special cases and, therefore, provides a unified description of black hole phase transitions in terms of curvature singularities.