An eikonal-inspired approach to the gravitational scattering waveform

A bstract We revisit the amplitude-based derivation of gravitational waveform for the scattering of two scalar black holes at subleading post-Minkowskian (PM) order. We take an eikonal-inspired approach to the two-massive-particle cut needed in the KMOC framework, as highlighted in 1, and show that its effect is to implement a simple change of frame. This clarifies one of the points raised in 2 when comparing with the post-Newtonian (PN) results. We then provide an explicit PM expression for the waveform in the soft limit, ω → 0, including the first non-universal, ω log ω, contribution. Focusing on this regime, we show that the small-velocity limit of our result agrees with the soft limit of the PN waveform of 2, provided that the two quantities are written in the same asymptotic frame. Performing the BMS supertranslation that, as discussed in 3, is responsible for the O (G) static contribution to the asymptotic field employed in the PN literature, we find agreement between the amplitude-based and the PN soft waveform up to and including G 3 / c 5 order.