Restricted Maximin surfaces and HRT in generic black hole spacetimes

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 $C_\partial$. 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.