Quantum hair and the string-black hole correspondence

We consider a thought experiment in which an energetic massless string probes a 'stringhole' (a heavy string lying on the correspondence curve between strings and black holes) at large enough impact parameter for the regime to be under theoretical control. The corresponding, explicitly unitary, S-matrix turns out to be perturbatively sensitive to the microstate of the stringhole: in particular, at leading order in l(s)/b, it depends on a projection of the stringhole's Lorentz-contracted quadrupole moment. The string-black hole correspondence is therefore violated if one assumes quantum hair to be exponentially suppressed as a function of black-hole entropy. Implications for the information paradox are briefly discussed.