Abstract
Exploiting simple yet remarkable properties of relativistic gravitational scattering, we use first-order self-force (linear-in-mass-ratio) results to obtain arbitrary-mass-ratio results for the complete third-subleading post-Newtonian (4.5PN) corrections to the spin-orbit sector of spinning-binary conservative dynamics, for generic (bound or unbound) orbits and spin orientations. We thereby improve important ingredients of models of gravitational waves from spinning binaries, and we demonstrate the improvement in accuracy by comparing against aligned-spin numerical simulations of binary black holes.
Highlights
Introduction.—The success of gravitational-wave (GW) astronomy in the decade relies on significantly improved theoretical predictions of GW signals from coalescing binaries of spinning compact objects such as black holes (BHs)
In this Letter, we follow a line of reasoning which leads to a complete result for the sought-after N3LO-PN spin-orbit dynamics, requiring relatively little computational effort by building on a diverse array of previous results
The scattering-angle constraints imply that known first-order self-force results with spin [28,29,30] uniquely fix the full N3LO-PN spin-orbit dynamics for arbitrary mass ratios
Summary
Searches and inference analyses [3] and in the upcoming TEOBResumS waveform models [37,38]. Using existing self-force results, we are able to uniquely determine the N3LO-PN spin-orbit dynamics, as encoded in the gauge-invariant scattering angle. The mass dependence of the scattering angle.—The local-in-time conservative dynamics of a two-massivebody system (without spin or higher multipoles) is fully encoded in the system’s gauge-invariant scattering-angle function χðm; m2; v; bÞ [43,44]. This gives the angle χ by which both bodies are deflected in the center-of-mass frame, as a function of the masses ma (a 1⁄4 1, 2), the asymptotic relative velocity v, and the impact parameter b. Based on the structure of iterative solutions in the weakfield (post-Minkowskian) approximation, it has been argued in Section II of Ref. [25] that this function exhibits the following simple dependence on the masses (at fixed v and b), through the total mass M 1⁄4 m1 þ m2 and the symmetric mass ratio ν 1⁄4 m1m2=M2,
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