Post-Newtonian Waveforms from Spinning Scattering Amplitudes

TL;DR

This paper derives gravitational waveforms from spinning binary black holes using quantum scattering amplitudes, confirming their consistency with classical gravitational radiation calculations at various orders.

Contribution

It establishes a direct link between quantum scattering amplitudes and classical gravitational waveforms for spinning black hole binaries, including spin effects and velocity corrections.

Findings

Agreement of waveforms with effective worldline methods

Matching of radiation fields in no-spin limit

Waveforms derived from scattering amplitudes applicable to inspiraling binaries

Abstract

We derive the classical gravitational radiation from an aligned spin binary black hole on \textit{closed} orbits, using a dictionary built from the 5-point QFT scattering amplitude of two massive particles exchanging and emitting a graviton. We show explicitly the agreement of the transverse-traceless components of the radiative linear metric perturbations -- and the corresponding gravitational wave energy flux -- at future null infinity, derived from the scattering amplitude and those derived utilizing an effective worldline action in conjunction with multipolar post-Minkowskian matching. At the tree-level, this result holds at leading orders in the black holes' velocities and up to quadratic order in their spins. At sub-leading order in black holes' velocities, we demonstrate a matching of the radiation field for quasi-circular orbits in the no-spin limit. At the level of the radiation field, and to leading order in the velocities, there exists a one-to-one correspondence between the binary black hole mass and current quadrupole moments, and the scalar and linear-in-spin scattering amplitudes, respectively. Therefore, we show explicitly that waveforms, needed to detect gravitational waves from \textit{inspiraling} binary black holes, can be derived consistently, to the orders considered, from the classical limit of quantum \textit{scattering} amplitudes.