Decoding the Apparent Horizon: A Coarse-Grained Holographic Entropy

Abstract

When a black hole forms from collapse in a holographic theory, the information in the black hole interior remains encoded in the boundary. We prove that the area of the black hole's apparent horizon is precisely the entropy associated to coarse graining over the information in its interior, subject to knowing the exterior geometry. This is the maximum holographic entanglement entropy that is compatible with all classical measurements conducted outside of the apparent horizon. We identify the boundary dual to this entropy and explain why it obeys a Second Law of Thermodynamics.

4+1 pages, 2 figures; v4: typos fixed in equation (15)

References in corpus (15)

• Holographic representation of local bulk operators
• Causality & holographic entanglement entropy
• A holographic proof of the strong subadditivity of entanglement entropy
• Deriving covariant holographic entanglement
• Bulk locality from modular flow
• Constructing local bulk observables in interacting AdS/CFT
• Entropy, Extremality, Euclidean Variations, and the Equations of Motion
• Quasiclassical Coarse Graining and Thermodynamic Entropy
• The area of horizons and the trapped region
• Black Holes, AdS, and CFTs
• The Cauchy problem on a characteristic cone for the Einstein equations in arbitrary dimensions
• Black Hole Thermodynamics and Statistical Mechanics
• No Simple Dual to the Causal Holographic Information?
• Unitarity and the Hilbert space of quantum gravity
• Marginally Trapped Surfaces and AdS/CFT

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