Scattering of gravitational waves off spinning compact objects with an effective worldline theory

We study the process, within classical general relativity, in which an incident gravitational plane wave, of weak amplitude and long wavelength, scatters off a massive spinning compact object, such as black hole or neutron star. The asymptotic scattered considered here at linear order Newton's constant $G$ while higher orders object's multipole expansion, is valuable characterization response object to external fields. This coincides with ($\ensuremath{\hbar}\ensuremath{\rightarrow}0$) limit quantum four-point (object graviton in, out) Compton amplitude, tree (linear-in-$G$) level. Such tree-level amplitudes are key building blocks generalized-unitary-based approaches post-Minkowskian dynamics binaries objects. In this paper, we compute using effective worldline theory describe determined by action functional for translational rotational degrees freedom, including couplings spin-induced moments space-time curvature. work up levels quadratic-in-spin quadrupole cubic-in-spin octupole couplings, respectively involving Wilson coefficients ${C}_{2}$ ${C}_{3}$. For special case ${C}_{2}={C}_{3}=1$ corresponding hole, find agreement through between our previous conjectures arising from considerations scattering amplitudes. also present new results ${C}_{3}$, anticipating instructive comparisons theories.