  The S-matrix in gravitational high energy scattering is computed from the
region of large impact parameters b down to the regime where classical
gravitational collapse is expected to occur. By solving the equation of an
effective action introduced by Amati, Ciafaloni and Veneziano we find that the
perturbative expansion around the leading eikonal result diverges at a critical
value signalling the onset of a new regime. We then discuss the main features
of our explicitly unitary S-matrix down to the Schwarzschild's radius R=2G
s^(1/2), where it diverges at a critical value b ~ 2.22 R of the impact
parameter. The nature of the singularity is studied with particular attention
to the scaling behaviour of various observables at the transition. The
numerical approach is validated by reproducing the known exact solution in the
axially symmetric case to high accuracy.
