A Holographic Entanglement Entropy Conjecture for General Spacetimes

TL;DR

This paper proposes a new method to compute holographic entanglement entropy in general spacetimes by anchoring extremal surfaces to holographic screens, extending beyond the traditional AdS/CFT framework.

Contribution

It introduces a generalized holographic entanglement entropy conjecture using holographic screens, applicable to arbitrary spacetimes, including cosmological models.

Findings

Extremal surfaces anchored to holographic screens lie within a causal region.

The proposed measure satisfies strong subadditivity.

Supports applicability to non-AdS, cosmological spacetimes.

Abstract

We present a natural generalization of holographic entanglement entropy proposals beyond the scope of AdS/CFT by anchoring extremal surfaces to holographic screens. Holographic screens are a natural extension of the AdS boundary to arbitrary spacetimes and are preferred codimension 1 surfaces from the viewpoint of the covariant entropy bound. A broad class of screens have a unique preferred foliation into codimension 2 surfaces called leaves. Our proposal is to find the areas of extremal surfaces achored to the boundaries of regions in leaves. We show that the properties of holographic screens are sufficient to prove, under generic conditions, that extremal surfaces anchored in this way always lie within a causal region associated with a given leaf. Within this causal region, a maximin construction similar to that of Wall proves that our proposed quantity satisfies standard properties of entanglement entropy like strong subadditivity. We conjecture that our prescription computes entanglement entropies in quantum states that holographically define arbitrary spacetimes, including those in a cosmological setting with no obvious boundary on which to anchor extremal surfaces.