Radiation enhancement and "temperature" in the collapse regime of gravitational scattering

Abstract

We generalize the semiclassical treatment of graviton radiation to gravitational scattering at very large energies $\sqrt{s}\gg m_P$ and finite scattering angles $Θ_s$, so as to approach the collapse regime of impact parameters $b \simeq b_c \sim R\equiv 2G\sqrt{s}$. 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 $Θ_s\ll 1$ but, for sizeable angles $Θ_s(b)\leq Θ_c = O(1)$ 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 $b\to b_c^+$ we find a radiation enhancement due to large tidal forces, so that the whole energy is radiated off, with a large multiplicity $\langle N \rangle\sim Gs \gg 1$ 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 $\sqrt{s}$.