Soft gravitational radiation from multi-body collisions

Abstract

We derive a universal expression for the gravitational radiation energy spectrum $d{E}^{GW}/d\omega$ 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 $2\to N$ 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. $m+M\to m+M$ 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 $2\to 2$ 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.

22 pages, 2 figures

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