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Gravitational Bound Waveforms from Amplitudes

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arxiv 2402.00124 v2 pith:MHDLJ2N2 submitted 2024-01-31 hep-th gr-qc

Tim Adamo , Riccardo Gonzo , Anton Ilderton This is my paper
classification hep-thgr-qc
keywords boundamplitudesanalyticcontinuationenergygravitationalmultipolesscattering
verification ladder T0 review T1 audit T2 compute T3 formal
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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.

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