Horizon entropy from quantum gravity condensates

TL;DR

This paper constructs quantum gravity condensate states representing spherically symmetric horizons, derives their entanglement entropy, and recovers the Bekenstein-Hawking entropy formula, supporting the entanglement interpretation of black hole entropy.

Contribution

It introduces a method to model horizon geometries in quantum gravity without classical symmetry reduction, deriving entropy consistent with thermodynamics.

Findings

Horizon entanglement entropy matches Bekenstein-Hawking formula.

Reduced density matrix exhibits holographic behavior.

Supports entanglement entropy as explanation for black hole entropy.

Abstract

We construct condensate states encoding the continuum spherically symmetric quantum geometry of an horizon in full quantum gravity, i.e. without any classical symmetry reduction, in the group field theory formalism. Tracing over the bulk degrees of freedom, we show how the resulting reduced density matrix manifestly exhibits an holographic behavior. We derive a complete orthonormal basis of eigenstates for the reduced density matrix of the horizon and use it to compute the horizon entanglement entropy. By imposing consistency with the horizon boundary conditions and semiclassical thermodynamical properties, we recover the Bekenstein--Hawking entropy formula for any value of the Immirzi parameter. Our analysis supports the equivalence between the von Neumann (entanglement) entropy interpretation and the Boltzmann (statistical) one.