  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.
