# How is the Presence of Horizons and Localized Matter Encoded in the Entanglement Entropy?

## TL;DR

This paper explores how horizons and localized matter in AdS_3 gravity influence entanglement entropy, revealing universal patterns and encoding geometric features through entanglement measures in a holographic framework.

## Contribution

It provides universal expressions for entanglement entropy in AdS_3 with black holes and conical singularities, linking geometric features to entanglement patterns using holography.

## Key findings

- Horizon and matter presence affects entanglement entropy through enhancement or reduction.
- Entanglement entropy scales with area or volume depending on the perturbation.
- Distinct behaviors like exponential or periodic patterns in entanglement entropy indicate different bulk features.

## Abstract

Motivated by the new theoretical paradigm that views spacetime 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) S_E for the case of three-dimensional AdS (AdS_3) 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 AdS_3 vacuum, (ii) scaling as area/volume of the leading term of the perturbative expansion of S_E, (iii) exponential/periodic behaviour of S_E, (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 AdS_3 vacuum