



01494nas a2200181   4500008004100000245005100041210005100092260001500143300001100158490000700169520100800176100001401184700001701198700002501215700001901240700001601259856003701275       2020                        eng d00aMore of the Bulk from Extremal Area Variations0 aMore of the Bulk from Extremal Area Variations  c12/24/2020  a0470010 v383 a<p>It was shown recently, building on work of Alexakis, Balehowksy, and Nachman that the geometry of (some portion of) a manifold with boundary is uniquely fixed by the areas of a foliation of two-dimensional disk-shaped surfaces anchored to the boundary. In the context of AdS/CFT, this implies that (a portion of) a four-dimensional bulk geometry can be fixed uniquely from the entanglement entropies of disk-shaped boundary regions, subject to several constraints. In this Note, we loosen some of these constraints, in particular allowing for the bulk foliation of extremal surfaces to be local and removing the constraint of disk topology; these generalizations ensure uniqueness of more of the deep bulk geometry by allowing for e.g. surfaces anchored on disconnected asymptotic boundaries, or HRT surfaces past a phase transition. We also explore in more depth the generality of the local foliation requirement, showing that even in a highly dynamical geometry like AdS-Vaidya it is satisfied.</p>1 aBao, Ning1 aCao, ChunJun1 aFischetti, Sebastian1 aPollack, Jason1 aZhong, Yibo  uhttps://arxiv.org/abs/2009.07850