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