Interactions between AdS black hole molecules

We take a bottom-up approach to find the interaction potential between the anti-de Sitter (AdS) black hole molecules under mean-field approximation. We start with the equation of state of dyonic AdS black holes in a fixed charge ensemble and use the method of classical cluster expansion to find the mean-field potential. We show that the Lennard-Jones (LJ) potential is a feasible choice to describe the equation of state. The LJ potential describes a two-body interaction. There exists a critical distance r0 such that two interacting particles repel (attract) each other for r r0 (r r0). We compute the value of r0 for dyonic AdS black holes and compare the result obtained from the Ruppeiner scalar curvature. Our analysis shows how the electric (and magnetic) charge affects the interaction between black hole molecules.

Automated summary

Using a bottom-up approach, we found the interaction potential between anti-de Sitter black hole molecules under mean-field approximation, with the Lennard-Jones potential describing the equation of state. The analysis shows the critical distance for two interacting particles, and compares the results with the Ruppeiner scalar curvature to understand how electric and magnetic charges affect the interaction between black hole molecules.