About gravitational-wave generation by a three-body system

We highlight some subtleties that affect naive implementations of quadrupolar and octupolar gravitational waveforms from numerically-integrated trajectories of three-body systems. Some of those subtleties arise from the requirement that the source be contained in its "coordinate near zone" when applying the standard PN formulae for gravitational-wave emission, and from the need to use the non-linear Einstein equations to correctly derive the quadrupole emission formula. We show that some of these subtleties were occasionally overlooked in the literature, with consequences for published results. We also provide prescriptions that lead to correct and robust predictions for the waveforms computed from numerically-integrated orbits.