Gravitational Bremsstrahlung in black-hole scattering at $$ \mathcal{O}\left({G}^3\right) $$: linear-in-spin effects

A bstract We compute the far-field time-domain waveform of the gravitational waves produced in the scattering of two spinning massive objects. The results include linear-in-spin ( S ) couplings and first-order gravitational corrections ( G 3 ), and are valid for encounters in the weak-field regime. Employing a field-theory framework based on the scattering of massive scalar and vector particles coupled to Einstein-Hilbert gravity, we derive results for leading and the next-to-leading spectral waveforms. We provide analytic expressions for the required scattering data, which include trees, one-loop amplitudes and their cuts. The expressions are extracted from numerical amplitude evaluations with the C aravel program, using analytic reconstruction techniques applied in the classical limit. We confirm a recent prediction for infrared physics of the classical observable, and observe the surprising appearance of a ultraviolet singularity, which drops out in the far-field waveform.