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Islands Far Outside the Horizon
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abstract
Information located in an entanglement island in semiclassical gravity can be nonperturbatively reconstructed from distant radiation, implying a radical breakdown of effective field theory. We show that this occurs well outside of the black hole stretched horizon. We compute the island associated to large-angular momentum Hawking modes of a four-dimensional Schwarzschild black hole. These modes typically fall back into the black hole but can be extracted to infinity by relativistic strings or, more abstractly, by asymptotic boundary operators constructed using the timelike tube theorem. Remarkably, we find that their island can protrude a distance of order $\sqrt{\ell_p r_{\rm hor}}$ outside the horizon. This is parametrically larger than the Planck scale $\ell_p$ and is comparable to the Bohr radius for supermassive black holes. Therefore, in principle, a distant observer can determine experimentally whether the black hole information paradox is resolved by complementarity, or by a firewall.
Forward citations
Cited by 6 Pith papers
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Firewalls From General Covariance
State-dependent horizon normalcy requires either a preferred global time, violating general covariance, or a dependence on the infinite future of the Hawking radiation.
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Quantum uncertainty in the area of a black hole
The variance of the Schwarzschild horizon area in linearized quantum gravity is computed to be ~ r_H^2 l_P^2, giving a standard deviation ∆A ~ r_H l_P.
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The mini-Page Curve in Cosmology
In 2D centaur geometries the entropy difference of a modular-conjugate Hawking-pair probe traces an inverse mini-Page curve that bottoms at τ≈β/8, marking when information begins to leave the cosmological horizon.
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An apologia for islands
Entanglement islands and Page curves can arise in massless gravity without an external bath, and compactly supported gauge-invariant operators exist in islands around generic symmetry-breaking black hole backgrounds.
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JT gravity and deformed CFTs
Deformed CFTs on a strip with a stretched-horizon conformal boundary are proposed as UV completions of pure and matter-coupled JT gravity, reproducing its entropy and a Page-curve-like saturation.
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Replica Wormholes, Modular Entropy, and Capacity of Entanglement in JT Gravity
In JT gravity toy models, late-time modular entropy and capacity of entanglement scale inversely with n times the inverse temperature, supporting a thermal reading of the replica parameter.
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