  We establish a connection between the ultra-Planckian scattering amplitudes
in field and string theory and unitarization by black hole formation in these
scattering processes. Using as a guideline an explicit microscopic theory in
which the black hole represents a bound-state of many soft gravitons at the
quantum critical point, we were able to identify and compute a set of
perturbative amplitudes relevant for black hole formation. These are the
tree-level N-graviton scattering S-matrix elements in a kinematical regime
(called classicalization limit) where the two incoming ultra-Planckian
gravitons produce a large number N of soft gravitons. We compute these
amplitudes by using the Kawai-Lewellen-Tye relations, as well as scattering
equations and string theory techniques. We discover that this limit reveals the
key features of the microscopic corpuscular black hole N-portrait. In
particular, the perturbative suppression factor of a N-graviton final state,
derived from the amplitude, matches the non-perturbative black hole entropy
when N reaches the quantum criticality value, whereas final states with
different value of N are either suppressed or excluded by non-perturbative
corpuscular physics. Thus we identify the microscopic reason behind the black
hole dominance over other final states including non-black hole classical
object. In the parameterization of the classicalization limit the scattering
equations can be solved exactly allowing us to obtain closed expressions for
the high-energy limit of the open and closed superstring tree-level scattering
amplitudes for a generic number N of external legs. We demonstrate matching and
complementarity between the string theory and field theory in different large-s
and large-N regimes.
