Black hole thermodynamics as seen through a microscopic model of a relativistic Bose gas

TL;DR

This paper models black hole horizons as a relativistic Bose gas, deriving quantization of horizon area and entropy, and explaining their proportionality, with some deviations from the standard constant.

Contribution

It introduces a microscopic Bose gas model for black hole horizons that predicts area quantization and entropy proportionality, extending previous thermodynamic analogies.

Findings

Horizon area and entropy are quantized according to Bekenstein's rule.

The model reproduces the proportionality between horizon area and entropy.

The proportionality constant differs from the canonical 1/4 value.

Abstract

Equations of gravity when projected on spacetime horizons resemble Navier-Stokes equation of a fluid with a specific equation of state [1-3]. We show that this equation of state describes massless ideal relativistic gas. We use these results, and build an explicit and simple molecular model of the fluid living on the Schwarzschild and Reissner-Nordstr\"om black hole horizons. For the spin zero Bose gas, our model makes two predictions: (i) The horizon area/entropy is quantized as given by Bekenstein's quantization rule, (ii) The model explains the correct type of proportionality between horizon area and entropy. However, for the physically relevant range of parameters, the proportionality constant is never equal to 1/4.