Refinement of the Bousso-Engelhardt Area Law

TL;DR

This paper proves a stronger area law for holographic screens, showing that subregions of leaves also have monotonic area growth when translated along a specific foliation.

Contribution

It introduces a new area law demonstrating that subregions of holographic screen leaves have monotonic area increase along leaf-orthogonal curves.

Findings

Subregions of leaves exhibit monotonic area growth.

A family of leaf-orthogonal curves (fibration) is constructed.

Area monotonicity extends to subregions of holographic screen leaves.

Abstract

Past holographic screens are codimension-one surfaces of indefinite signature that are foliated by marginally anti-trapped surfaces called leaves. Future holographic screens are defined similarly except with marginally trapped leaves. Bousso and Engelhardt recently showed that the leaves of past and future holographic screens have monotonic area. We prove a stronger area law that shows that subregions of leaves also have monotonic area. For every past and future holographic screen, there exists a family of leaf-orthogonal curves called the fibration of the screen. Any region in a leaf can be translated along the fibration to a leaf of larger area. Our result states that the area of the subregion grows as it is translated.