Abstract
The phase structure of Kerr-AdS black holes is studied at three different temperatures, $T_{c1}$, $T_{c2}$ and $T_L$. At $T_{c1}$, a second order phase transition is identified to be in the same universality class as the van der Waals liquid-gas system. We derive the critical exponents ($\alpha$, $\beta$, $\gamma$, $\delta$)=(0, $\frac{1}{2}$, 1, 3) associated to this phase transition, and discuss the free energy and the scaling symmetry near the critical point. $T_L$ is the lowest temperature under which a Kerr-AdS black hole could reduce to a Schwarzschild-AdS black hole, and this temperature correspond to the critical temperature determined in the Hawking-Page phase transition. $T_{c2}$ is the temperature which separates the stable and partially unstable isotherms. Along with $T_{c2}$, we found an asymptotic value of angular momentum $\Omega_0$ = $1/l$ as $J$ goes to infinity. This asymptotic value reminisces us the minimal value of the molecule volume $V_0$ in the van der Waals liquid-gas system.