Islands Far Outside the Horizon

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 information paradox is resolved by
complementarity, or by a firewall.