A Mean-Field Description for AdS Black Hole

TL;DR

This paper develops a mean-field model that accurately describes the thermodynamics of asymptotically AdS black holes across dimensions, linking them to interacting particle systems and microstructures.

Contribution

It introduces a mean-field potential framework that maps AdS black hole thermodynamics to an interacting particle gas, revealing a microstructure interpretation in 3+1 dimensions.

Findings

Thermodynamics of AdS black holes matches that of a mean-field particle system.

In 3+1 dimensions, black holes are modeled as interacting microstructures.

The mean-field description is valid in the high temperature limit across dimensions.

Abstract

In this paper we find an equivalent mean-field description for asymptotically $AdS$ black hole in high temperature limit and in arbitrary dimensions. We obtain a class of mean-field potential for which the description is valid. We explicitly show that there is an one to one correspondence between the thermodynamics of a gas of interacting particles moving under a mean-field potential and an $AdS$ black hole, namely the equation of state, temperature, pressure, entropy and enthalpy of both the systems match. In $3+1$ dimensions, in particular, the mean-field description can be thought of as an ensemble of tiny interacting {\it asymptotically flat} black holes moving in volume $V$ and at temperature $T$. This motivates us to identify these asymptotically flat black holes as microstructure of asymptotically $AdS$ black holes in $3+1$ dimensions.