Towards the intermolecular force in charged AdS black hole

Abstract

In this paper we attempt to find the intermolecular force of charged AdS black holes (BH). We first write the equation of state of BH in the form of the van der Waals (vdW) equation and show that this equation describes accurately the BH phase transition. Based on the Lennard- Jones (LJ) potential we establish the modified LJ force which is compatible with this vdW equation. Of particular interest, in the first time we find that this force can be always written as the sum of the topological force, created by the topological charge, and the electrostatic force, created by charged conducting micro-sphere with definite radius. Then the phase transition of BH is totally controlled by these forces. In the process of phase transition from small to large BHs the sum of these forces changes from repulsive to attractive forces and this behavior is supported by the scalar curvature of the thermodynamic geometry. Combining these properties, we arrive at the physical picture of the BH molecules: they behave like charged conducting micro-spheres which bear topological charge. It necessarily to remark that although our intermolecular force is better than the one obtained recently in [29], it remains an approximate force.