Radiation enhancement and temperature in the collapse regime of gravitational scattering

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 sqrt(s). Our basic tool is the extension of the recently proposed, unified form of radiation to the Amati Ciafaloni Veneziano (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 → bc+ , 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 1/R. The latter corresponds to the Hawking temperature for a black hole of mass notably smaller than sqrt(s).