Complementarity + Back-reaction is enough

We investigate a recent development of the black hole information problem, in which a practical paradox has been formulated to show that complementarity is insufficient. A crucial ingredient in this practical paradox is to distill information from the early Hawking radiation within the past lightcone of the black hole. By causality this action can back-react on the black hole. Taking this back-reaction into account, the paradox could be resolved without invoking any new physics beyond complementarity. This resolution requires a certain constraint on the S-matrix to be satisfied. Further insights into the S-matrix could potentially be obtained by effective-field-theory computations of the back-reaction on the nice slice.