More of the Bulk from Extremal Area Variations

TL;DR

This paper extends previous results on bulk geometry determination from boundary entanglement by relaxing constraints, allowing for more general extremal surfaces, and demonstrating the approach's applicability in dynamic geometries like AdS-Vaidya.

Contribution

It generalizes the uniqueness of bulk geometry reconstruction by removing topological and foliation constraints, enabling broader applications in holography.

Findings

Uniqueness of bulk geometry is maintained with local extremal surface foliations.

The approach applies to disconnected boundaries and phase transitions.

Local foliation condition holds in dynamic AdS-Vaidya geometries.

Abstract

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.