Exploring an S-matrix for gravitational collapse

We analyze further a recently proposed S-matrix description of transplanckian scattering in the specific case of axisymmetric collisions of extended sources, where some of the original approximations are not necessary. We confirm the claim that such an approximate description appears to capture the essential features of (the quantum counterpart of) classical gravitational collapse. More specifically, the S-matrix develops singularities whose location in the sources' parameter space are consistent with (and numerically close to) the bounds coming from closed-trapped-surface collapse criteria. In the vicinity of the critical "lines" the phase of the elastic S-matrix exhibits a universal fractional-power behaviour reminiscent of Choptuik's scaling near critical collapse.