Tidal effects on radiation in gravitational shockwave collisions

Abstract

We compute high frequency gravitational wave radiation in shockwave collisions of a light mass compact object with energy $\mu_L$ off a heavy compact object (black hole) with energy $\mu_H \gg \mu_L$. A formal solution is obtained in terms of shockwave propagators that provide snapshots of $O(\mu_L\mu_H^n)$ tidal response functions sensitive to classical and potentially semi-classical dynamics of black hole formation. In a perturbative expansion, the first nontrivial contribution of $O(\mu_L\mu_H)$ is the emission of a graviton from the Lipatov vertex generated by the fusion of two reggeized gravitons. For graviton frequencies $\omega\rightarrow 0$, the Lipatov amplitude reduces to the ultrarelativistic limit of the single-graviton exchange Weinberg amplitude. At $O(\mu_L\mu_H^2)$, the Lipatov amplitude includes a piece accounting for the rescattering of the graviton off a reggeized graviton and another, corresponding to graviton emission from a vertex fusing three reggeized gravitons. These nontrivial contributions again simplify to the Weinberg radiative amplitude for two-graviton exchange in the soft limit. We highlight throughout double copy structures to gluon radiation in dilute-dense collisions of Yang-Mills shockwaves. We relate our shockwave results to the eikonal multiple scattering framework of Veneziano et al.