Abstract
The AdS/CFT understanding of CFT entanglement is based on HRT surfaces in the dual bulk spacetime. While such surfaces need not exist in sufficiently general spacetimes, the maximin construction demonstrates that they can be found in any smooth asymptotically locally AdS spacetime without horizons or with only Kasner-like singularities. In this work, we introduce restricted maximin surfaces anchored to a particular boundary Cauchy slice C∂ . We show that the result agrees with the original unrestricted maximin prescription when the restricted maximin surface lies in a smooth region of spacetime. We then use this construction to extend the existence theorem for HRT surfaces to generic charged or spinning AdS black holes whose mass-inflation singularities are not Kasner-like. We also discuss related issues in time-independent charged wormholes.
Highlights
The full array of possible spacetimes have not yet been explored
We show that the result agrees with the original unrestricted maximin prescription when the restricted maximin surface lies in a smooth region of spacetime
We consider restricted maximin surfaces — defined by bulk Cauchy surfaces Σ that intersect the AlAdS boundary on a fixed boundary Cauchy surface C∂ — and show that they must agree with HRT surfaces when they lie in a smooth region of the spacetime
Summary
This section will discuss restricted maximin surfaces. In a different context, a maximin construction that fixes the entire boundary of a (in that case partial) Cauchy surface was used in [15]. The restricted maximin surface MR(A, C∂) is defined as the min(A, Σ, C∂) whose area is maximal with respect to variations of Σ that preserve C∂. We use ΣMR(A,C∂) to denote a Cauchy surface on which MR(A, C∂) is minimal. When ΣMR(A,C∂) is both spacelike and smooth, this follows by the technical argument in section 3.5 of [7]. We show that the restricted maximin surface MR(A, C∂) is an HRT surface for every choice of C∂ that contains A so long as MR(A, C∂) lies in a smooth region of the bulk spacetime. As noted in [7] (theorem 3), since the bulk satisfies NCC and the boundary of the future contains only null geodesics without conjugate points, the focusing theorem [17] guarantees the representative to have no more area than x(A). Area[MR(A, C∂)] ≤ Area[xΣ(A)] ≤ Area[x(A)], and MR(A, C∂) is a least-area extremal surface
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