Interaction Between AdS Black Hole Molecules

TL;DR

This paper models the interactions between AdS black hole molecules using a mean-field approach, identifying a Lennard-Jones potential that captures their behavior and analyzing how charges influence these interactions.

Contribution

It introduces a novel mean-field potential model for AdS black hole molecules based on classical cluster expansion and Lennard-Jones potential fitting.

Findings

Lennard-Jones potential effectively describes black hole molecule interactions.

Critical distance r_0 determines repulsive or attractive forces.

Electric and magnetic charges significantly affect interaction dynamics.

Abstract

We take a bottom-up approach to find the interaction potential between the $AdS$ black hole molecules under mean-field approximation. We start with the equation of state of dyonic $AdS$ black holes in 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 $r_0$ such that two interacting particles repel (attract) each other for $r < r_0$ ($r > r_0$). We compute the value of $r_0$ for dyonic $AdS$ black holes and compare the result obtained from the Ruppeiner scalar curvature. Our analysis shows how the electric (and magnetic) charge effects the interaction between black hole molecules.