Thermodynamic geometry and phase transition of spinning AdS black holes

Employing the thermodynamic geometry approach, we explore phase transition of four dimensional spinning black holes in an anti-de Sitter (AdS) spaces and found the following novel results. (i) Contrary to the charged AdS black hole, thermodynamic curvature of the spinning AdS black hole diverges at the critical point, without needing normalization.(ii) There is a certain region with small entropy in the space of parameters for which the thermodynamic curvature is positive and the repulsive interaction dominates. Such behavior exists even when the pressure is extremely large. (iii) The dominant interactions in the microstructure of extremal spinning AdS black holes are strongly repulsive, which is similar to an ideal gas of fermions at zero temperature. (iv) The maximum of thermodynamic curvature, $ \left\vert R\right\vert $, is equal to $C_{{}_{P}}$ maximum values for the Van der Waals fluid in the supercritical region. While for the black hole, they are close to each other near the critical point.