Post-Newtonian multipoles from the next-to-leading post-Minkowskian gravitational waveform

Abstract

We consider the frequency-domain leading order and next-to-leading order post-Minkowskian waveforms obtained from the tree-level and one-loop amplitudes describing the scattering of two massive scalar objects and the emission of one graviton. We explicitly calculate their post-Newtonian (PN) limit obtaining an expansion up to the third subleading PN order in all ingredients: the tree-level amplitude, the odd and even parts of the real one-loop kernel, and the Compton or “rescattering” cuts, thus reaching 3PN precision for the latter. We provide explicit expressions for the multipole decomposition of these results in the center-of-mass frame and compare them with the results obtained from the classical multipolar post-Minkowskian method. We find perfect agreement between the two, once the Bondi-Metzner-Sachs supertranslation frame is properly adjusted and the infrared divergences due to rescattering are suitably subtracted in dimensional regularization. This shows that the approach proposed in Georgoudis et al. [An eikonal-inspired approach to the gravitational scattering waveform, J. High Energy Phys. 03 (2024) 089] can be applied beyond the soft-regime ensuring the agreement between amplitude-based and multipolar post-Minkowskian results for generic frequencies.