Soft gravitational radiation from multi-body collisions

TL;DR

This paper derives a universal formula for gravitational radiation emitted during multi-particle collisions, including sub-leading corrections, and explores specific cases like elastic and inelastic scattering of massive bodies, with implications for gravitational wave physics.

Contribution

It provides the first comprehensive expression for sub-leading order gravitational radiation spectrum in generic multi-body collisions, including quantum spin effects.

Findings

All sub-leading $ ext{O}( ext{omega})$ contributions cancel in elastic scattering of two massive bodies.

Inelastic scattering with sub-leading soft gravitons results in a non-zero radiation flux.

The results have potential applications in understanding gravitational waves from black hole collisions.

Abstract

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. $m+M\rightarrow m+M$ with $m,M$ the masses of the two bodies respectively. We demonstrate that in this case all $\mathcal{O}(\omega)$ contributions to the energy flux exactly cancel each others. Nevertheless, we also show that, for a $2\rightarrow 2$ 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 Holes' collisions with possible testable implications in gravitational waves physics.