Why is the black hole entropy (almost) linear in the horizon area?

Abstract

We show that essentially pure classical thermodynamics is sufficient to determine Bekenstein's formula for the black hole's entropy, $S=\eta A$. We base our reasoning on the minimal assumption that since black body radiation is describable by classical thermodynamics, so is the complete black hole-Hawking radiation system. Furthermore, we argue that any non-linear correction to the black hole entropy must be quantum mechanical in nature. The proportionality coefficient, $\eta=1/4\ell_P^2$, must be calculated within a semi-classical or full-fledged quantum mechanical framework.