Quantum tunneling and unitarity features of an S-matrix for gravitational collapse

Starting from the semiclassical reduced-action approach to transplanckian scattering by Amati, Veneziano and one of us and from our previous quantum extension of that model, we investigate the S-matrix expression for inelastic processes by extending to this case the tunneling features previously found in the region of classical gravitational collapse. The resulting model exhibits some non-unitary S-matrix eigenvalues for impact parameters b < b(c), a critical value of the order of the gravitational radius R = 2G root s, thus showing that some (inelastic) unitarity defect is generally present, and can be studied quantitatively. We find that S-matrix unitarity for b < b(c) is restored only if the rapidity phase-space parameter y is allowed to take values larger than the effective coupling Gs/(h) over bar itself. Some features of the resulting unitary model are discussed.