Unitary Constraints on Semiclassical Schwarzschild Black Holes in the Presence of Island

Abstract

We reconsider $D\ge 4$ dimensional asymptotically flat eternal Schwarzschild black hole, and focus on the situation where the inner boundary of the radiation region is chosen to be near the horizon (i.e. $\beta \ll 1$). The tension between the near-horizon condition and the short-distance approximation emerges in large dimensions in $[JHEP06(2020)085]$. We remove this tension by introducing a more proper near horizon condition, thus the resulting island solution is well-behaved in any $D\ge 4$ dimensional spacetime. Interestingly, a novel constraint is obtained in this situation as required by the existence of the island solution, which directly leads to the constraints on the size of the Schwarzschild black hole, the position of the inner boundary for the radiation region, or the value of $c\cdot {\tilde{G}}_N$ in any $D\ge 4$ dimension. When considering the large $D$ limit, the constraint on the size of the Schwarzschild black hole obtained in this situation is in agreement with the result given in $[Phys.Rev.D102(2020)2,026016]$. We interpret these as the unitary constraints implied by the presence of island in semiclassical gravity.

arXiv comment21 pages, 4 figures; improvements to the expression; Footnote 2 added to show a new analytical island solution for $n\to \infty$ while $\alpha \sim \beta /n$; accepted for publication in PRD

References in corpus (47)

• Holographic Derivation of Entanglement Entropy from AdS/CFT
• Entropy and Area
• A Covariant Holographic Entanglement Entropy Proposal
• Black holes as mirrors: quantum information in random subsystems
• Information in Black Hole Radiation
• Evanescent Black Holes
• Fast Scramblers
• 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
• Black Hole Entropy in Canonical Quantum Gravity and Superstring Theory
• Entanglement entropy in free quantum field theory
• Time Dependence of Hawking Radiation Entropy
• Massive Islands
• Information Transfer with a Gravitating Bath
• Entanglement islands in higher dimensions
• The large D limit of General Relativity
• Inconsistency of Islands in Theories with Long-Range Gravity
• Islands in Schwarzschild black holes
• Page Curve for an Evaporating Black Hole
• Islands in Asymptotically Flat 2D Gravity
• Entanglement and alpha entropies for a massive scalar field in two dimensions
• Critical Islands
• Large D gravity and low D strings
• Notes on islands in asymptotically flat 2d dilaton black holes
• Island in the Presence of Higher Derivative Terms
• Island in Charged Black Holes
• Information Flow in Black Hole Evaporation
• Islands and Page curves of Reissner-Nordström black holes
• Replica wormholes for an evaporating 2D black hole
• Islands in charged linear dilaton black holes
• Islands and stretched horizon
• Effective entropy of quantum fields coupled with gravity
• The universality of islands outside the horizon
• Entanglement entropy of asymptotically flat non-extremal and extremal black holes with an island
• Islands in Linear Dilaton Black Holes
• Islands in Kaluza-Klein black holes
• Island, Page Curve and Superradiance of Rotating BTZ Black Holes
• Unitarity of Entanglement and Islands in Two-Sided Janus Black Holes
• Warped Information and Entanglement Islands in AdS/WCFT
• Island and Page curve for one-sided asymptotically flat black hole
• Mutual information, islands in black holes and the Page curve
• Page Curves of Reissner-Nordström Black Hole in HD Gravity
• Entanglement entropy and vacuum states in Schwarzschild geometry
• Black hole evaporation and semiclassicality at large D

Cited by in corpus (11)

• The Markov gap in the presence of islands
• Ownerless island and partial entanglement entropy in island phases
• Page curves and Entanglement Islands for the Step-Function Vaidya Model of Evaporating Black Holes
• Mutual information of subsystems and the Page curve for Schwarzschild de-Sitter black hole
• Island of Reissner-Nordstr$\ddot{\mathbf{o}}$m anti-de Sitter black holes in the large $d$ limit
• Towards bit threads in general gravitational spacetimes
• Effect of backreaction on Island, Page curve and Mutual Information
• Information paradox and island of covariant black holes in LQG
• Island rules for the noncommutative black hole
• Island of acoustic black hole in Schwarzschild spacetime
• Thermodynamics and information recovery of Schwarzschild AdS black holes in conformal Killing gravity