Gravitational Bound Waveforms from Amplitudes

Abstract

With the aim of computing bound waveforms from scattering amplitudes, we explore gravitational two-body dynamics using the Schwinger-Dyson equations and Bethe-Salpeter recursion. We show that the tree-level scattering waveform admits a natural analytic continuation, in rapidity, to the bound waveform, which we confirm from an independent calculation, in the Post-Newtonian expansion, of the time-domain multipoles at large eccentricity. We demonstrate consistency of this scattering-to-bound map with the Damour-Deruelle prescription for orbital elements in the quasi-Keplerian parametrization (which enters into the evaluation of the multipoles) and with the analytic continuation, in the binding energy, of radiated energy and angular momentum at 3PM.

46 pages, 10 figures; v2: typos corrected, references added

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Cited by in corpus (13)

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• Black hole scattering near the transition to plunge: Self-force and resummation of post-Minkowskian theory
• Classifying post-Minkowskian geometries for gravitational waves via loop-by-loop Baikov
• The spinning self-force EFT: 1SF waveform recursion relation and Compton scattering
• Dirac brackets for classical radiative observables
• Bootstrapping spinning two body problem in dynamical Chern-Simons gravity using worldline QFT
• The gravitational Compton amplitude from flat and curved spacetimes at second post-Minkowskian order
• Gravitational radiation from hyperbolic orbits: comparison between self-force, post-Minkowskian, post-Newtonian, and numerical relativity results
• The first law of binary black hole scattering
• Relieving scale disparity in binary black hole simulations
• On-shell approach to scalar hair in spinning binaries
• Constants of motion in gravitational self-force theory
• Resummed energy loss in extreme-mass-ratio scattering using critical orbits