The microscopic structure of charged AdS black hole

The microscopic structure of charged anti-de Sitter (AdS) black holes remains a fascinating subject in modern gravitational physics. In this paper, we investigate the phase transition mechanism and the underlying microstructure of charged AdS black holes by integrating a modified Lennard-Jones (LJ) potential with Ruppeiner thermodynamic geometry. Unlike previous studies, we explicitly incorporate the topological charge [Formula: see text] alongside the electric charge Q into the microscopic interaction model. We demonstrate that the black hole constituents behave as “positive topological ions,” where the topological charge acts as a coupling parameter regulating the depth of the attractive potential well. This phenomenological model is rigorously validated by the Ruppeiner scalar curvature, which exhibits a consistent transition from attraction ([Formula: see text]) to repulsion ([Formula: see text]). Furthermore, we report that the number density ratio at the critical point is [Formula: see text], distinct from the standard Van der Waals hard-sphere value of 3.0. This deviation suggests that the black hole micromolecules possess a specific “soft-core” nature governed by the gauge-gravity coupling.