Resummed spinning waveforms from five-point amplitudes

TL;DR

This paper develops a method to compute gravitational waveforms from spinning black hole scattering using five-point amplitudes, valid for arbitrary spins and including spin effects up to fourth order.

Contribution

It introduces a novel approach to derive waveforms from five-point amplitudes with no spin expansion, incorporating contact terms for spinning particles, applicable to Kerr black holes.

Findings

Waveforms valid up to fourth order in spin.

A new form of spinning Compton amplitude with contact terms.

Agreement with gravitational memory formulas to all orders in spin.

Abstract

We compute the classical tree-level five-point amplitude for the two-to-two scattering of spinning celestial objects with the emission of a graviton. Using this five-point amplitude, we then turn to the computation of the leading-order time-domain gravitational waveform. The method we describe is suitable for arbitrary values of classical spin of Kerr black holes and does not require any expansion in powers of the spin. In this paper we illustrate it in the simpler case of the scattering of one Kerr and one Schwarzschild black hole. An important ingredient of our calculation is a novel form of the Compton amplitude with spinning particles including contact terms derived from matching to black-hole perturbation theory calculations. This ensures that our waveform is valid up to at least fourth order in the spin. Our method can be applied immediately to generate improved waveforms once higher-order contact terms in the Compton amplitude become available. Finally, we show the formula for the gravitational memory to all orders in the spin, which is in agreement with our results.