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We present a natural generalization of holographic entanglement entropyproposals beyond the scope of AdS/CFT by anchoring extremal surfaces toholographic screens. Holographic screens are a natural extension of the AdSboundary to arbitrary spacetimes and are preferred codimension 1 surfaces fromthe viewpoint of the covariant entropy bound. A broad class of screens have aunique preferred foliation into codimension 2 surfaces called leaves. Ourproposal is to find the areas of extremal surfaces achored to the boundaries ofregions in leaves. We show that the properties of holographic screens aresufficient to prove, under generic conditions, that extremal surfaces anchoredin this way always lie within a causal region associated with a given leaf.Within this causal region, a maximin construction similar to that of Wallproves that our proposed quantity satisfies standard properties of entanglemententropy like strong subadditivity. We conjecture that our prescription computesentanglement entropies in quantum states that holographically define arbitraryspacetimes, including those in a cosmological setting with no obvious boundaryon which to anchor extremal surfaces.

A Holographic Entanglement Entropy Conjecture for General Spacetimes