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

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.