TY - JOUR
T1 - Towards bulk metric reconstruction from extremal area variations
AU - Bao, Ning
AU - Cao, Chunjun
AU - Fischetti, Sebastian
AU - Keeler, Cynthia
N1 - Publisher Copyright:
© 2019 IOP Publishing Ltd.
PY - 2019
Y1 - 2019
N2 - The Ryu-Takayanagi and Hubeny-Rangamani-Takayanagi formulae suggest that bulk geometry emerges from the entanglement structure of the boundary theory. Using these formulae, we build on a result of Alexakis, Balehowsky, and Nachman to show that in four bulk dimensions, the entanglement entropies of boundary regions of disk topology uniquely fix the bulk metric in any region foliated by the corresponding HRT surfaces. More generally, for a bulk of any dimension d ≥ 4, knowledge of the (variations of the) areas of twodimensional boundary-anchored extremal surfaces of disk topology uniquely fixes the bulk metric wherever these surfaces reach. This result is covariant and not reliant on any symmetry assumptions; its applicability thus includes regions of strong dynamical gravity such as the early-time interior of black holes formed from collapse. While we only show uniqueness of the metric, the approach we present provides a clear path towards an explicit spacetime metric reconstruction.
AB - The Ryu-Takayanagi and Hubeny-Rangamani-Takayanagi formulae suggest that bulk geometry emerges from the entanglement structure of the boundary theory. Using these formulae, we build on a result of Alexakis, Balehowsky, and Nachman to show that in four bulk dimensions, the entanglement entropies of boundary regions of disk topology uniquely fix the bulk metric in any region foliated by the corresponding HRT surfaces. More generally, for a bulk of any dimension d ≥ 4, knowledge of the (variations of the) areas of twodimensional boundary-anchored extremal surfaces of disk topology uniquely fixes the bulk metric wherever these surfaces reach. This result is covariant and not reliant on any symmetry assumptions; its applicability thus includes regions of strong dynamical gravity such as the early-time interior of black holes formed from collapse. While we only show uniqueness of the metric, the approach we present provides a clear path towards an explicit spacetime metric reconstruction.
KW - AdS/CFT
KW - boundary rigidity
KW - bulk reconstruction
KW - holographic entanglement entropy
UR - http://www.scopus.com/inward/record.url?scp=85073070695&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=85073070695&partnerID=8YFLogxK
U2 - 10.1088/1361-6382/ab377f
DO - 10.1088/1361-6382/ab377f
M3 - Article
AN - SCOPUS:85073070695
SN - 0264-9381
VL - 36
JO - Classical and Quantum Gravity
JF - Classical and Quantum Gravity
IS - 18
M1 - 185002
ER -