How is the Presence of Horizons and Localized Matter Encoded in the Entanglement Entropy?
arXiv:1703.02505 · doi:10.1142/S0217751X1750083X
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
16 pages, no figures
References in corpus (8)
- Towards a derivation of holographic entanglement entropy
- Near Extremal Black Hole Entropy as Entanglement Entropy via AdS2/CFT1
- Entwinement and the emergence of spacetime
- Entanglement between the future and past in the quantum vacuum
- Entanglement entropy of black holes and AdS/CFT correspondence
- Entanglement entropy of two-dimensional Anti-de Sitter black holes
- Entanglement thermodynamics for charged black holes
- Holographic Dual to Conical Defects III: Improved Image Method