Area Law Unification and the Holographic Event Horizon

TL;DR

This paper establishes new area laws for generalized holographic screens in general relativity, linking their geometry to outer entropy and providing a holographic dual for event horizon geometry in spherically symmetric spacetimes.

Contribution

It introduces a broad family of area laws for untrapped surfaces, extending known laws for holographic screens and horizons, and connects these to holographic entropy concepts.

Findings

New area laws for generalized holographic screens.

Relation between screen geometry and outer entropy in holography.

Holographic dual description of event horizon geometry.

Abstract

We prove a new, large family of area laws in general relativity, which apply to certain classes of untrapped surfaces that we dub generalized holographic screens. Our family of area laws contains, as special cases, the area laws for marginally-trapped surfaces (holographic screens) and the event horizon (Hawking's area theorem). In addition to these results in general relativity, we show that in the context of holography the geometry of a generalized holographic screen is related to the outer entropy of the screen. Specifically, we show for spherically-symmetric spacetimes that the area of the largest HRT surface consistent with the outer wedge can be computed in terms of the geometry of the general (not necessarily marginally-trapped) codimension-two surface defining the wedge. This outer entropy satisfies a second law of thermodynamics, growing monotonically along the generalized holographic screen. In particular, this result provides the holographic dual for the geometry of the event horizon for spherically-symmetric spacetimes.