Entanglement entropy in curved spacetimes with event horizons

TL;DR

This paper calculates the entanglement entropy in curved spacetimes with horizons, specifically in cosmological models like the Friedmann-Robertson-Walker universe, using a Hamiltonian and numerical lattice approach.

Contribution

It introduces a Hamiltonian method and numerical lattice computations for entanglement entropy in curved spacetimes with horizons, focusing on cosmological models.

Findings

Entanglement entropy scales as 0.30 r_H^2/a^2 in the studied models.

Results resemble flat space formulas despite the curved background.

Provides explicit calculations for the FRW universe.

Abstract

We consider the computation of the entanglement entropy in curved backgrounds with event horizons. We use a Hamiltonian approach to the problem and perform numerical computations on a spherical lattice of spacing $a$. We study the cosmological case and make explicit computations for the Friedmann-Robertson-Walker universe. Our results for a massless, minimally coupled scalar field can be summarized by $S_{ent}=0.30 r_H^2/a^2$,which resembles the flat space formula, although here the horizon radius, $r_H$, is time-dependent.