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.

Figure 1

Semiclassical Hawking temperature ($T$) and specific heat ($C_{\Omega }$) vs entropy ($S$) for fixed $\Omega =0.3$.

Figure 2

Volume expansion coefficient ($\alpha$) and compressibility ($k_T$) vs entropy ($S$) for fixed $\Omega =0.3$.

Figure 3

Thermodynamic scalar curvature ($R$) vs entropy ($S$): $\Omega =0.3$ in (a) and $\Omega =1.5$ in (b).