Soft gravitational radiation from multi-body collisions

Abstract We derive a universal expression for the gravitational radiation energy spectrum dE GW /dω at sub-leading order emitted from a generic gravitational hard scattering of multi-particles or multi-bodies. Our result includes all O $$ \mathcal{O} $$ (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 $$ \mathcal{O} $$ (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 Hole collisions with possible testable implications in gravitational waves physics