Soft gravitational radiation from multi-body collisions

Understand

We derive a universal expression for the gravitational radiation energy spectrum $dE^{GW}/d\omega$ at sub-leading order emitted from a generic gravitational hard scattering of multi-particles or multi-bodies.

• Our result includes all $\mathcal{O}(\omega)$ corrections to the gravitational radiation flux from a generic $2\rightarrow N$ collision, in both the cases of massless and massive particles/bodies.
• We also show the dependence of the radiation energy fluxby 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.