Unitarity alternatives in the reduced-action model for gravitational collapse

Based on the ACV approach to transplanckian energies, the reduced-action model for the gravitational S-matrix predicts a critical impact parameter bc ∼ R ≡ 2G√s such that S-matrix unitarity is satisfied in the perturbative region b > bc, while it is exponentially suppressed with respect to s in the region b < bc that we think corresponds to gravitational collapse. Here we definitely confirm this statement by a detailed analysis of both the critical region b ≃ bc and of further possible contributions due to quantum transitions for b < bc. We point out, however, that the subcritical unitarity suppression is basically due to the boundary condition which insures that the solutions of the model be ultraviolet-safe. As an alternative, relaxing such condition leads to solutions which carry short-distance singularities presumably regularized by the string. We suggest that through such solutions — depending on the detailed dynamics at the string scale — the lost probability may be recovered.