Homology Conditions for RT Surfaces in Double Holography

Abstract

Recently, a novel formula for computing entropy in theories coupled to semi-classical gravity has been devised. Using this so-called island formula the entropy of semi-classical black holes follows a Page curve. Here, we study the relation between this novel entropy and semi-classical entropy in the context of doubly-holographic models. Double holography allows for two different $d$-dimensional descriptions of a black hole coupled to a non-gravitational bath, both of which allow a holographic computation of von Neumann entropy in bath subregions. We argue that the correct homology constraint for Ryu-Takayanagi surfaces depends on which of those $d$-dimensional perspectives is taken. As a consequence the von Neumann entropies of a fixed subregion in both descriptions can disagree. We discuss how the von Neumann entropies in both descriptions are related to the entropy computed by the island formula and coarse grained entropy. Moreover, we argue that the way operators transform between the two descriptions depends on their complexity. A simple toy model is introduced to demonstrate that a sufficiently complicated map between two descriptions of the system can give rise to an island formula and wormholes. Lastly, we speculate about the relation between double-holography and black hole complementarity.

25 pages, 9 figures; v2: references added, improved abstract; v3: new title, several clarifications, version to be published in CQG

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• BCFT in a Black Hole Background: An Analytical Holographic Model
• Page Curve of Effective Hawking Radiation
• JT Gravity from Partial Reduction and Defect Extremal Surface
• Holographic duals of evaporating black holes
• Entanglement entropy analysis of dyonic black holes using doubly holographic theory
• Defect extremal surfaces for entanglement negativity
• Black Hole and de Sitter Microstructures from a Semiclassical Perspective
• Effective Action, Spectrum and First Law of Wedge Holography
• Holographic Coarse-Graining: Correlators from the Entanglement Wedge and Other Reduced Geometries
• Entropy of Radiation with Dynamical Gravity
• Reflected Entropy and Entanglement Negativity for Holographic Moving Mirrors
• Holographic scattering and non-minimal RT surfaces
• Exploring causality in braneworld/cutoff holography via holographic scattering
• Entanglement Entropy and Thermal Phase Transitions from Curvature Singularities
• Page Curve of AdS-Vaidya Model for Evaporating Black Holes
• Spacing Statistics of Energy Spectra: Random Matrices, Black Hole Thermalization, and Echoes