Area Law Unification and the Holographic Event Horizon

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.

41 pages, 8 figures

References in corpus (8)

• $\mathcal{N}=1$ supersymmetric indices and the four-dimensional A-model
• Deriving covariant holographic entanglement
• Pulling the Boundary into the Bulk
• The Cauchy problem on a characteristic cone for the Einstein equations in arbitrary dimensions
• Angular momentum conservation for dynamical black holes
• Spacetime from Unentanglement
• The Boundary of the Future
• Deformation of Codimension-2 Surface and Horizon Thermodynamics

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• Holographic Shannon Entropy: The Outer Entropy of Entanglement Wedges