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We find S-matrix evidence that longitudinal string spreading can induce interactions between early and late time systems in the near-horizon region of a black hole. By generalizing the effect to closed strings and performing an eikonal resummation, we find a tractable regime where these interactions become strong at a Schwarzschild time separation Δt rₛ. We estimate the mutual information in a scenario analogous to Hayden-Preskill, and we find that string spreading is sufficient in itself for a late-time detector to recover a significant fraction of the information encoded in an infaller's state. Interesting open directions include analysis of the interaction of the detector with Unruh radiation (which may introduce noise that somewhat degrades the recovery), and formulating the optimal detector setup including many entangled detectors (which could further increase the information recovery by enhancing sensitivity to kinematic parameters with subleading dependence in the amplitude).
Mousatov et al. (Thu,) studied this question.