Entropy and black hole horizons

TL;DR

This paper offers a statistical mechanical derivation of black hole entropy in two and four dimensions by counting eigenmodes near the horizon, explaining its order and independence from field degrees of freedom.

Contribution

It introduces a simple method based on eigenmode counting to derive black hole entropy, clarifying its fundamental properties.

Findings

Reproduces Bekenstein entropy formula in four dimensions

Derives two-dimensional black hole entropy expression

Shows entropy is of order 1/ħ and independent of field count

Abstract

The standard approach of counting the number of eigenmodes of $N$ scalar fields near the horizon is used as a basis to provide a simple statistical mechanical derivation of the black hole entropy in two and four dimensions. The Bekenstein formula $S={A\ov 4G\h}$ and the two-dimensional entropy $S=2M/\l\h $ are naturally obtained (up to a numerical constant of order 1). This approach provides an explanation on why the black hole entropy is of order $1/\h $ and why it is independent of the number of field-theoretical degrees of freedom.