Towards an S-matrix Description of Gravitational Collapse

Extending our previous results on trans-Planckian ($Gs\gg \mathrm{\hslash }$) scattering of light particles in quantum string-gravity we present a calculation of the corresponding S-matrix from the region of large impact parameters ($b \gg G\sqrt{s}>\lambda_s$) down to the regime where classical gravitational collapse is expected to occur. By solving the semiclassical equations of a previously introduced effective-action approximation, we find that the perturbative expansion around the leading eikonal result diverges at a critical value $b = b_c = O(G\sqrt{s})$, signalling the onset of a new (black-hole related?) regime. We then discuss the main features of our explicitly unitary S-matrix – and of the associated effective metric – down to (and in the vicinity of) $b = b_c$,andpresentsomeideasandresultsonitsextensionallthewaytothe$ b \to 0$region\mathrm{.}Wefindthatfor$b<b_c$ the physical field solutions are complex-valued and the S-matrix shows additional absorption, related to a new production mechanism. The field solutions themselves are, surprisingly, everywhere regular, suggesting a quantum-tunneling – rather than a singular-geometry – situation.