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

TL;DR

This paper uses the radial distribution function to explore the mesostructure of AdS black holes, revealing phase-dependent arrangements of black hole molecules and linking mesostructure changes to phase transitions.

Contribution

It introduces the radial distribution function as a novel tool to probe the mesostructure of AdS black holes and connects mesostructure behavior with phase transitions.

Findings

Mesostructure behaves as an ideal gas at high temperature.

Small black holes exhibit liquid-like mesostructure.

Large black holes exhibit gas-like mesostructure.

Abstract

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.