The radial distribution function reveals the underlying mesostructure of the AdS black hole

A bstract Based on the equations of state, one can infer underlying interaction potentials among black hole molecules in case Schwarzschild-AdS and charged AdS holes. The microscopic with potential arrange a specific way to form mesostructure, whose size is between macro (black system) micro molecules). As result, mesostructure leads emergence macroscopic phase. However, information about are still elusive. In this paper, radial distribution function introduced probe hole. We find that behaves as ideal gas when temperature high. Furthermore, we for liquid-like (gas-like) phase small (large) sudden change emerges from gas-like undergoes transition large hole, consistent viewpoint reminiscent vdW fluid. This study provides new angle towards understanding its mesostructure.