Restricted Maximin surfaces and HRT in generic black hole spacetimes

TL;DR

The work addresses when HRT surfaces exist and correctly compute entanglement entropy in generic AdS spacetimes, including charged or rotating black holes with non-Kasner singularities. It introduces restricted maximin surfaces anchored to a boundary slice $C_\partial$ and proves that, if these surfaces lie in smooth bulk regions, they coincide with the standard HRT surfaces, extending Wall's maximin framework. Using this construction, the authors prove the existence of HRT surfaces for AdS-RN-like spacetimes and more general charged or rotating black holes with mass-inflation singularities, and they establish strong subadditivity within this setting. They also discuss time-independent charged wormholes and argue that HRT surfaces persist in appropriate geometric regions, reinforcing the holographic entanglement entropy prescription with $S_A = \frac{\operatorname{Area}[\operatorname{ext}(A)]}{4G}$ in a broad class of spacetimes.

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.

Figures (3)

• Figure 1: The maximal analytic extension of the AdS-Reissner-Nordström black hole. for our study in Section \ref{['sec:existence']} we truncate it to the AdS-hyperbolic unshaded region between the past and future (AdS-) Cauchy horizons (heavy dashed lines).
• Figure 2: Perturbed one-sided (left) and two-sided (right) AdS-RN black holes. The null parts are mass-inflation singularities. A spacelike piece of the singularity forms whenever caustics arise on a null singularity. Such caustics always arise in the one-sided case, and also occur for strong enough perturbations (as shown here) in the two-sided case. The resulting spacelike singularities should be Kasner-like, as can be seen from the fact that the region between the inner- and outer-horizons in figure \ref{['fig:AdSRN']} admits a foliation by spatially homogenous slices that, when subjected to correspondingly homogeneous perturbations, becomes precisely an AdS-Kasner solution. Sufficiently close to a curvature singularity, one should be able to treat any solution as approximately homogeneous, so the spacelike part of the singularity should again be Kasner-like. In the left panel, the black hole is formed by a collapsing shell (in blue).
• Figure 3: Time-independent charged wormhole which is constructed by sewing two AdS-RN spacetimes together along a domain wall (thick line). Due to the internal infinities (small circles), the Cauchy horizons are union of the Cauchy horizons of the two AdS-RN spacetimes. Limits of Cauchy surfaces like the one shown (red) can reach such horizons.