Marginally Trapped Surfaces and AdS/CFT

TL;DR

This paper explores the relationship between marginally trapped surfaces in AdS spacetimes and holographic entanglement entropy, establishing bounds, divergences, and monotonicity properties relevant to the dual CFT.

Contribution

It demonstrates that boundary-anchored marginally trapped surfaces lie between causal and extremal surfaces, linking their area to coarse-grained entropy and extending holographic entropy bounds.

Findings

Boundary-anchored leaves are between causal and extremal surfaces.

Area divergence matches that of extremal surfaces at leading order.

Leaf areas increase monotonically along holographic screens.

Abstract

It has been proposed that the areas of marginally trapped or anti-trapped surfaces (also known as leaves of holographic screens) may encode some notion of entropy. To connect this to AdS/CFT, we study the case of marginally trapped surfaces anchored to an AdS boundary. We establish that such boundary-anchored leaves lie between the causal and extremal surfaces defined by the anchor and that they have area bounded below by that of the minimal extremal surface. This suggests that the area of any leaf represents a coarse-grained von Neumann entropy for the associated region of the dual CFT. We further demonstrate that the leading area-divergence of a boundary-anchored marginally trapped surface agrees with that for the associated extremal surface, though subleading divergences generally differ. Finally, we generalize an argument of Bousso and Engelhardt to show that holographic screens with all leaves anchored to the same boundary set have leaf-areas that increase monotonically along the screen, and we describe a construction through which this monotonicity can take the more standard form of requiring entropy to increase with boundary time. This construction is related to what one might call future causal holographic information, which in such cases also provides an upper bound on the area of the associated leaves.