Thermodynamic Geometry of Black Holes in the Canonical Ensemble

Understand

We investigate the thermodynamics and critical phenomena for four dimensional RN-AdS and Kerr-AdS black holes in the canonical ensemble both for the normal and the extended phase space employing the framework of thermodynamic geometry.

• The thermodynamic scalar curvatures for these black holes characterizes the liquid-gas like first order phase transition analogous to the van der Waals fluids, through the $R$-Crossing Method.
• It is also shown that the thermodynamic scalar curvatures diverge as a function of the temperature at the critical point.