Black Hole Entropy and Induced Gravity

TL;DR

This paper discusses how black hole entropy can be understood as entanglement entropy arising from quantum correlations, with the effective gravitational constant's renormalization linking matter fields to the Bekenstein-Hawking entropy, supporting the induced gravity perspective.

Contribution

It argues that black hole entropy is primarily entanglement entropy and supports the induced gravity framework where the gravitational action emerges from quantum fluctuations.

Findings

Black hole entropy is linked to entanglement entropy.

The renormalized gravitational constant depends on matter field content.

Induced gravity explains black hole entropy as pure entanglement entropy.

Abstract

In this short essay we review the arguments showing that black hole entropy is, at least in part, ``entanglement entropy", i.e., missing information contained in correlations between quantum field fluctuations inside and outside the event horizon. Although the entanglement entropy depends upon the matter field content of the theory, it turns out that so does the Bekenstein-Hawking entropy $A/4\hbar G_{ren}$, in precisely the same way, because the effective gravitational constant $G_{ren}$ is renormalized by the very same quantum fluctuations. It appears most satisfactory if the entire gravitational action is ``induced", in the manner suggested by Sakharov, since then the black hole entropy is purebred entanglement entropy, rather than being hybrid with bare gravitational entropy (whatever that might be.)