Second order phase transition and thermodynamic geometry in Kerr-AdS black holes

We discuss a scheme based on Ehrenfest-like equations to exhibit and classify transitions between two phases (with ``smaller'' and ``larger'' masses) of Kerr-AdS black holes. We show that for fixed angular velocity this phase transition is of second order as both Ehrenfest's equations are satisfied. Finally, we make a close connection of the results found from this analysis with those obtained from the thermodynamic state space geometry approach.