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Title:
Islands Far Outside the Horizon
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Abstract:
Information located in an entanglement island in semiclassical gravity can benonperturbatively reconstructed from distant radiation, implying a radicalbreakdown of effective field theory. We show that this occurs well outside ofthe black hole stretched horizon. We compute the island associated tolarge-angular momentum Hawking modes of a four-dimensional Schwarzschild blackhole. These modes typically fall back into the black hole but can be extractedto infinity by relativistic strings or, more abstractly, by asymptotic boundaryoperators constructed using the timelike tube theorem. Remarkably, we find thattheir 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 experimentallywhether the black hole information information paradox is resolved bycomplementarity, or by a firewall.
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