Spinning waveforms from KMOC at leading order

TL;DR

This paper derives an analytic time-domain waveform for Kerr black hole scattering at leading order, incorporating high-order spins, using a novel formalism that simplifies calculations by leveraging analyticity and known amplitudes.

Contribution

It generalizes the KMOC formalism to radiative observables and introduces a new approach to include higher-order spin effects in gravitational waveforms.

Findings

Derived explicit waveform expressions for spinning black hole scattering.

Introduced a gauge-invariant form of the Kovacs-Thorne waveform.

Enabled easier inclusion of higher-order spin effects.

Abstract

We provide the analytic waveform in time domain for the scattering of two Kerr black holes at leading order in the post-Minkowskian expansion and up to fourth order in both spins. The result is obtained by the generalization of the KMOC formalism to radiative observables, combined with the analytic continuation of the five-point scattering amplitude to complex kinematics. We use analyticity arguments to express the waveform directly in terms of the three-point coupling of the graviton to the spinning particles and the gravitational Compton amplitudes, completely bypassing the need to compute and integrate the five-point amplitude. In particular, this allows to easily include higher-order spin contributions for any spinning compact body. Finally, in the spinless case we find a new compact and gauge-invariant representation of the Kovacs-Thorne waveform.