Post-Newtonian Waveforms from Spinning Scattering Amplitudes

Abstract

We derive the classical gravitational radiation from an aligned spin binary black hole on \textit{closed} orbits, using a dictionary built from the 5-point QFT scattering amplitude of two massive particles exchanging and emitting a graviton. We show explicitly the agreement of the transverse-traceless components of the radiative linear metric perturbations -- and the corresponding gravitational wave energy flux -- at future null infinity, derived from the scattering amplitude and those derived utilizing an effective worldline action in conjunction with multipolar post-Minkowskian matching. At the tree-level, this result holds at leading orders in the black holes' velocities and up to quadratic order in their spins. At sub-leading order in black holes' velocities, we demonstrate a matching of the radiation field for quasi-circular orbits in the no-spin limit. At the level of the radiation field, and to leading order in the velocities, there exists a one-to-one correspondence between the binary black hole mass and current quadrupole moments, and the scalar and linear-in-spin scattering amplitudes, respectively. Therefore, we show explicitly that waveforms, needed to detect gravitational waves from \textit{inspiraling} binary black holes, can be derived consistently, to the orders considered, from the classical limit of quantum \textit{scattering} amplitudes.