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.

21 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

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• 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