Unitarity alternatives in the reduced-action model for gravitational collapse

Understand

Based on the ACV approach to transplanckian energies, the reduced-action model for the gravitational S-matrix predicts a critical impact parameter b_c ~ R = 2 G 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.