Entanglement entropy in curved spacetimes with event horizons

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 ${\mathit{S}}_{\mathrm{ent}}$=0.30${\mathit{r}}_{\mathit{H}}^2$/${\mathit{a}}^2$, which resembles the flat space formula, although here the horizon radius ${\mathit{r}}_{\mathit{H}}$ is time dependent.