Bekenstein-Hawking entropy from Criticality

TL;DR

This paper models black hole horizon thermodynamics using a fluid analogy, demonstrating how Bekenstein-Hawking entropy emerges from a critical phase transition in a (2+1)-dimensional fluid system, with a negative cosmological constant influencing the phase structure.

Contribution

It introduces a statistical mechanical model of the black hole horizon-fluid that reproduces Bekenstein-Hawking entropy through critical phenomena and phase transitions.

Findings

Bekenstein-Hawking entropy derived from horizon-fluid model.

Negative cosmological constant induces a tri-critical point.

Phase transition behavior analogous to Landau mean field theory.

Abstract

Vacuum Einstein equations when projected on to a black hole horizon is analogous to the dynamics of fluids. In this work we address the question, whether certain properties of semi-classical black holes could be holographically mapped into properties of (2 + 1)-dimensional fluid living on the horizon. In particular, we focus on the statistical mechanical description of the horizon-fluid that leads to Bekenstein-Hawking entropy. Within the paradigm of Landau mean field theory and existence of a condensate at a critical temperature, we explicitly show that Bekenstein-Hawking entropy and other features of black hole thermodynamics can be recovered from the statistical modelling of the fluid. We also show that a negative cosmological constant acts like an external magnetic field that induces order in the system leading to the appearance of a tri-critical point in the phase diagram.