Statistical and entanglement entropy for black holes in quantum geometry

TL;DR

This paper demonstrates that in loop quantum gravity, entanglement entropy and statistical mechanical entropy of black hole horizons are equivalent, with quantum geometry mediating correlations at the Planck scale.

Contribution

It establishes the equivalence of entanglement and statistical entropy for black holes within the isolated horizon framework of loop quantum gravity.

Findings

Entanglement and statistical entropy coincide for black holes in loop quantum gravity.

Quantum geometry at Planck scale mediates correlations across the horizon.

The structure of horizon eigenstates links geometric and entanglement entropy.

Abstract

We analyze the relationship between entanglement (or geometric) entropy with statistical mechanical entropy of horizon degrees of freedom when described in the framework of isolated horizons in loop quantum gravity. We show that, once the relevant degrees of freedom are identified, the two notions coincide. The key ingredient linking the two notions is the structure of quantum geometry at Planck scale implied by loop quantum gravity, where correlations between the inside and outside of the black hole are mediated by eigenstates of the horizon area operator.