Alan Zeng

We derive a universal expression for the gravitational radiation energy spectrum dE /dω at sub-leading order emitted from a generic gravitational hard scattering of multi-particles or multi-bodies. Our result includes all O(ω) corrections to the gravitational radiation flux from a generic 2 → N collision, in both the cases of massless and massive particles/bodies. We also show the dependence of the radiation energy flux by the quantum spin in case of particle collisions. Then, we consider the specific case of a gravitational elastic scattering of two massive bodies, i.e. m+M → m+M with m,M the masses of the two bodies respectively. We demonstrate that in this case all O(ω) contributions to the energy flux exactly cancel each others. Nevertheless, we also show that, for a 2 → 2 inelastic scattering, the inclusion of sub-leading soft gravitons leads to a not zero radiation flux, having a simple expression in certain asymptotic regimes. Our results can be applied to the case of Black H...