Phase Transition in Conjugate Planes of Charged AdS Black Hole

We study possible patterns of phase transitions at finite temperature in the charged AdS black holes (BHs). It is shown that in corresponding to standard pairs of conjugate thermodynamic variables charged AdS black holes contains either critical phenomena or interesting phase behaviour: a) for volume vs. pressure (V, P)  a first order phase transition occurs similar to the van der Waals like from liquid to gas; b) for electric potential vs. charge (\Phi, Q)  a first order phase transition associated with the electric charge instability. The distinction between them is characterized by the behaviors of the phase diagrams, the phase transition regions, the latent heats, the coexistence lines and the scalar curvatures associating with different Riemann spaces established in BH thermodynamic geometry approach. We conjecture that this scenario could become realistic for all other black holes.