Thermodynamic Geometry and Phase Transitions in Kerr-Newman-AdS Black Holes

Understand

We investigate phase transitions and critical phenomena in Kerr-Newman-Anti de Sitter black holes in the framework of the geometry of their equilibrium thermodynamic state space.

• The scalar curvature of these state space Riemannian geometries is computed in various ensembles.
• The scalar curvature diverges at the critical point of second order phase transitions for these systems.
• Remarkably, however, we show that the state space scalar curvature also carries information about the liquid-gas like first order phase transitions and the consequent instabilities and phase coexistence for these black holes.