On the Intermolecular Forces of Charged AdS Black Holes and Charged AdS White Holes

This paper consists of two parts. In the first part, we attempt to find the intermolecular force of charged AdS black hole (BH). Starting from the fact that the equation of states of BH and the van der Waals (vdW) equation have the same compressibility factors , we determine the intermolecular force of BH. We find that this force can always be written as the sum of the topological force created by the topological charge, and the electrostatic force created by the conducting microsphere charged with the electric charge. This is the intermolecular force for all systems whose phase transition possesses the same compressibility factor . In part 2 we begin with the equation of state of white hole (WH) whose temperature is negative and find that its compressibility factor is equal to, and, at the same time, we establish the anti- vdW equation with compressibility factor . This is the main factor for us to determine the intermolecular force of WH. This force is composed of two terms. The first term is the repulsive force, created by the topological charge, and the second term exhibits the attractive electrostatic force, created by two quasi- Cooper pairs (similar to Cooper pairs in the superconductors) consisting of two charged spheric molecules with electric charge. The formation of quasi-Cooper pairs is by BH a quantum effect which was realized in the process of quantum tunneling from BH to WH. At high temperature, the quasi-Cooper pairs are broken, leading to the cancellation of the attractive force, and the repulsive force will push all molecules of WH further and further away. The behaviors of BH force and WH force are totally suppoted by the corresponding scalar curvatures of the thermodynamic geometry. Keywords: Intermolecular force, charged AdS black hole, white hole, quantum tunneling, topological force, phase transition.