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The AdS/CFT understanding of CFT entanglement is based on HRT surfaces in thedual bulk spacetime. While such surfaces need not exist in sufficiently generalspacetimes, the maximin construction demonstrates that they can be found in anysmooth asymptotically locally AdS spacetime without horizons or with onlyKasner-like singularities. In this work, we introduce restricted maximinsurfaces anchored to a particular boundary Cauchy slice $C_\partial$. We showthat the result agrees with the original unrestricted maximin prescription whenthe restricted maximin surface lies in a smooth region of spacetime. We thenuse this construction to extend the existence theorem for HRT surfaces togeneric charged or spinning AdS black holes whose mass-inflation singularitiesare not Kasner-like. We also discuss related issues in time-independent chargedwormholes.

Restricted Maximin surfaces and HRT in generic black hole spacetimes