Post-Newtonian Multipoles from the Next-to-Leading Post-Minkowskian Gravitational Waveform

Understand

We consider the frequency-domain LO and NLO post-Minkowskian (PM) 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 (MPM) method.
• We find perfect agreement between the two, once the BMS supertranslation frame is properly adjusted and the infrared divergences due to rescattering are suitably subtracted in dimensional regularization.