Black hole entropy and the holographic principle

TL;DR

This paper reviews black hole properties and discusses how their entropy relates to the holographic principle, suggesting that the fundamental degrees of freedom of a region are proportional to its surface area, not volume.

Contribution

It synthesizes classical, quantum, and thermodynamic aspects of black holes and highlights the holographic bound on entropy, emphasizing the area law for quantum degrees of freedom.

Findings

Black hole entropy is proportional to the event horizon area.

The holographic principle implies degrees of freedom scale with surface area.

Universal entropy bounds apply to regions of spacetime.

Abstract

Black holes monopolize nowadays the center stage of fundamental physics. Yet, they are poorly understood objects. Notwithstanding, from their generic properties, one can infer important clues to what a fundamental theory, a theory that includes gravitation and quantum mechanics, should give. Here we review the classical properties of black holes and their associated event horizons, as well as the quantum and thermodynamic properties, such as the temperature, derived from the Hawking radiation, and the entropy. Then, using the black hole properties we discuss a universal bound on the entropy for any object, or for any given region of spacetime, and finally we present the arguments, first given by 't Hooft, that, associating entropy with the number of quantum degrees of freedom, i.e., the logarithm of quantum states, via statistical physics, leads to the conclusion that the degrees of freedom of a given region are in the area A of the region, rather than in its volume V as naively could be thought. Surely, a fundamental theory has to take this in consideration.