Non-extremal Island in de Sitter Gravity
arXiv:2407.21617 · doi:10.1007/JHEP03(2025)004
Abstract
This paper investigates the challenges and resolutions in computing the entanglement entropy for the quantum field theory coupled to de Sitter (dS) gravity along a timelike boundary. The conventional island formula, originally designed to calculate the fine-grained entropy for a non-gravitational system coupled to anti-de Sitter (AdS) gravity, encounters difficulties in de Sitter gravitational spacetime, failing to provide a physically plausible extremal island. To overcome these problems, we introduce a doubly holographic model by embedding a dS braneworld in an AdS bulk spacetime. This approach facilitates the computation of entanglement entropy through holographic correlation functions, effectively circumventing the constraints of the island formula. We demonstrate that the correct recipe for calculating entanglement entropy with dS gravity involves the non-extremal island, whose boundary is instead defined at the edge of the dS gravitational region. Our findings indicate that, during the island phase, the entanglement wedge of the non-gravitational bath includes the entire dS gravitational space. Using the second variation formula, we further show that the existence of a locally minimal surface anchored on the gravitational brane is intrinsically linked to the extrinsic curvature of the brane.
64 pages, 20 figures; v2:added an important reference; v3: published version
References in corpus (55)
- Holographic Derivation of Entanglement Entropy from AdS/CFT
- Entanglement Entropy and Quantum Field Theory
- Non-Gaussian features of primordial fluctuations in single field inflationary models
- Aspects of Holographic Entanglement Entropy
- A Covariant Holographic Entanglement Entropy Proposal
- Entanglement entropy and conformal field theory
- The dS/CFT Correspondence
- Replica Wormholes and the Entropy of Hawking Radiation
- Quantum Extremal Surfaces: Holographic Entanglement Entropy beyond the Classical Regime
- Quantum corrections to holographic entanglement entropy
- The entropy of bulk quantum fields and the entanglement wedge of an evaporating black hole
- The Page curve of Hawking radiation from semiclassical geometry
- Locally Localized Gravity
- Open and Closed String Interpretation of SUSY CFT's on Branes with Boundaries
- Holographic Dual of BCFT
- Maximin Surfaces, and the Strong Subadditivity of the Covariant Holographic Entanglement Entropy
- AdS/CFT and gravity
- The Gravity Dual of a Density Matrix
- Causality & holographic entanglement entropy
- Aspects of AdS/BCFT
- Transcending the ensemble: baby universes, spacetime wormholes, and the order and disorder of black hole information
- On geodesic propagators and black hole holography
- Islands in cosmology
- Bra-ket wormholes in gravitationally prepared states
- The dS/dS Correspondence
- An Information Paradox and Its Resolution in de Sitter Holography
- Codimension two holography for wedges
- Holographic Pseudo Entropy
- Islands in de Sitter space
- Low-dimensional de Sitter quantum gravity
- Pseudo Entropy in dS/CFT and Time-like Entanglement Entropy
- De Sitter Holography and Entanglement Entropy
- Timelike entanglement entropy
- The First Law of Complexity
- BCFT and Islands in Two Dimensions
- Thermalization of the spectral function in strongly coupled two dimensional conformal field theories
- de Sitter space, extremal surfaces and "time-entanglement"
- Quasi-local energy and microcanonical entropy in two-dimensional nearly de Sitter gravity
- Pure de Sitter space and the island moving back in time
- Evolution of Two-Point Functions from Holography
- The Price of Curiosity: Information Recovery in de Sitter Space
- Holography in de Sitter Space via Chern-Simons Gauge Theory
- Aspects of The First Law of Complexity
- No Page Curves for the de Sitter Horizon
- Island Finder and Entropy Bound
- Brane Dynamics of Holographic BCFTs
- Islands in Closed and Open Universes
- Zoo of holographic moving mirrors
- An Outsider's Perspective on Information Recovery in de Sitter Space
- Encoding beyond cosmological horizons in de Sitter JT gravity
- Closed universes in two dimensional gravity
- Island formula in Planck brane
- Bridging the static patches: de Sitter holography and entanglement
- Gluing AdS/CFT
- On the Quantum Bousso Bound in JT gravity