Islands Far Outside the Horizon

TL;DR

This paper demonstrates that information from entanglement islands associated with Hawking radiation can be reconstructed from regions far outside the black hole horizon, challenging effective field theory and offering insights into the black hole information paradox.

Contribution

It computes the island for high-angular-momentum Hawking modes in a Schwarzschild black hole, showing the island can extend significantly outside the horizon, beyond Planck scale.

Findings

Island extends outside the horizon by a distance of order √(l_p r_hor).

Distant observers can, in principle, determine the resolution of the information paradox.

Challenges the effective field theory assumption near black holes.

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.