# Restricted Maximin surfaces and HRT in generic black hole spacetimes

## TL;DR

This paper extends the existence of HRT surfaces in AdS/CFT to more general black hole spacetimes using restricted maximin surfaces, including those with complex singularities, enhancing the understanding of entanglement in such geometries.

## Contribution

It introduces restricted maximin surfaces anchored to specific boundary slices and proves their equivalence to original maximin surfaces in smooth regions, extending HRT surface existence to complex black hole spacetimes.

## Key findings

- Extended HRT surface existence to generic charged/spinning black holes.
- Introduced restricted maximin construction for boundary-anchored surfaces.
- Discussed implications for time-independent charged wormholes.

## 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 $C_\partial$. 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.