The equal area law of asymptotically AdS black holes in extended phase space

According to Maxwell’s equal area law we study the “real” phase diagram of the charged AdS black hole and the Kerr-AdS black hole. In the extended phase space constructed by treating the cosmological constant as pressure, the two kinds of AdS black hole display themselves like van der Waals system. Under the critical temperature T _c , there exists a regime where the condition of stable equilibrium will be violated. We employ the equal area law to find an isobar which is the real two phase coexistence line. As a byproduct we find a simple method to derive the critical value of the thermodynamic quantities.