Unitarity alternatives in the reduced-action model for gravitational collapse

Abstract

Based on the ACV approach to transplanckian energies, the reduced-action model for the gravitational S-matrix predicts a critical impact parameter ${b_c} \sim R \equiv 2G\sqrt {s}$ such that S-matrix unitarity is satisfied in the perturbative region b > b _c , while it is exponentially suppressed with respect to s in the region b < b _c that we think corresponds to gravitational collapse. Here we definitely confirm this statement by a detailed analysis of both the critical region b ≃ b _c and of further possible contributions due to quantum transitions for b < b _c . 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.