How is the presence of horizons and localized matter encoded in the entanglement entropy?

Abstract

Motivated by the new theoretical paradigm that views space–time geometry as emerging from the entanglement of a pre-geometric theory, we investigate the issue of the signature of the presence of horizons and localized matter on the entanglement entropy (EE) [Formula: see text] for the case of three-dimensional AdS (AdS3) gravity. We use the holographically dual two-dimensional CFT on the torus and the related modular symmetry in order to treat bulk black holes and conical singularities (sourced by pointlike masses not shielded by horizons) on the same footing. In the regime where boundary tori can be approximated by cylinders, we are able to give universal expressions for the EE of black holes and conical singularities. We argue that the presence of horizons/localized matter in the bulk is encoded in the EE in terms of (i) enhancement/reduction of the entanglement of the AdS3 vacuum, (ii) scaling as area/volume of the leading term of the perturbative expansion of [Formula: see text], (iii) exponential/periodic behavior of [Formula: see text] and (iv) presence of unaccessible regions in the noncompact/compact dimension of the boundary cylinder. In particular, we show that the reduction effect of matter on the entanglement of the vacuum found by Verlinde for the de Sitter vacuum extends to the AdS3 vacuum.