We generalize the semiclassical treatment of graviton radiation to
gravitational scattering at very large energies √s≫mP and finite
scattering angles Θs, so as to approach the collapse regime of impact
parameters b≃bc∼R≡2G√s. Our basic tool is the
extension of the recently proposed, unified form of radiation to the ACV
reduced-action model and to its resummed-eikonal exchange. By superimposing
that radiation all-over eikonal scattering, we are able to derive the
corresponding (unitary) coherent-state operator. The resulting graviton
spectrum, tuned on the gravitational radius R, fully agrees with previous
calculations for small angles Θs≪1 but, for sizeable angles
Θs(b)≤Θc=O(1) acquires an exponential cutoff of the
large ωR region, due to energy conservation, so as to emit a finite
fraction of the total energy. In the approach-to-collapse regime of
b→b+c we find a radiation enhancement due to large tidal forces, so
that the whole energy is radiated off, with a large multiplicity
⟨N⟩∼Gs≫1 and a well-defined frequency cutoff of order R−1.
The latter corresponds to the Hawking temperature for a black hole of mass
notably smaller than √s.
