High post-Minkowskian gravitational waveform for hyperbolic encounters in the extreme-mass-ratio limit

TL;DR

This paper computes high-precision gravitational waveforms for hyperbolic encounters in the extreme-mass-ratio limit up to the fifth post-Minkowskian order, providing benchmarks for future calculations and insights into gravitational wave memory.

Contribution

It presents the first computation of the scattering waveform at 4PM and 5PM orders, extending previous results and offering new benchmarks for multiloop quantum amplitude calculations.

Findings

Waveform computed up to 5PM order in the frequency domain.

Agreement between quantum amplitude and traditional methods at 3PM order.

Improved estimates of radiated energy up to 6PN level.

Abstract

The frequency-domain waveform emitted by a two-body scattering process is computed in the extreme-mass-ratio limit through the fifth post-Minkowskian (PM) order (i.e., $O(G^5)$) and the fractional sixth post-Newtonian (PN) order. The current accuracy of the scattering waveform obtained by quantum amplitude methods is the one-loop level corresponding to the 3PM order, whereas the 4PM waveform is known up to the 2PN order only as derived within the traditional multipolar-post-Minkowskian formalism. Direct comparison between these waveforms to the first order in the mass ratio shows that they differ at most by the effect of an angular-independent time shift, leading to a complete physical agreement at the same level of accuracy. The new results at the 4PM and 5PM orders thus provide a benchmark for future multiloop calculations. The soft limit of the waveform at the leading order in the small-frequency expansion gives the gravitational wave memory, which is evaluated at the 4PM and 5PM orders. The waveform is also used to obtain the radiated energy at $O(G^6)$, improving its knowledge from 3PN to 6PN level.