Why the Entropy of a Black Hole is $A/4$?

TL;DR

This paper explores why black hole entropy is universally proportional to surface area, proposing that the internal dynamical degrees of freedom and their temperature dependence explain the exact $A/4$ relation.

Contribution

It introduces a perspective linking the universality of black hole entropy to the temperature-dependent parameters of internal dynamical degrees of freedom.

Findings

The entropy $S_H$ is connected to dynamical degrees of freedom.

The universality of $S_H$ is restored when considering temperature dependence.

The exact $A/4$ entropy value emerges from this temperature-dependent framework.

Abstract

A black hole considered as a part of a thermodynamical system possesses the Bekenstein-Hawking entropy $S_H =A_H /(4l_{\mbox{\scriptsize{P}}}^2)$, where $A_H$ is the area of a black hole surface and $l_{\,\mbox{\scriptsize{P}}}$ is the Planck length. Recent attempts to connect this entropy with dynamical degrees of freedom of a black hole generically did not provide the universal mechanism which allows one to obtain this exact value. We discuss the relation between the 'dynamical' contribution to the entropy and $S_H$, and show that the universality of $S_H$ is restored if one takes into account that the parameters of the internal dynamical degrees of freedom as well as their number depends on the black hole temperature.