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Applying the effective-source approach to frequency-domain self-force calculations for eccentric orbits

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arxiv 2306.17221 v2 pith:LQY4KH63 submitted 2023-06-29 gr-qc

Benjamin Leather , Niels Warburton This is my paper · ORCID
classification gr-qc
keywords calculationsapproacheffective-sourceorbitssecond-orderself-forcedomaineccentric
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Extreme mass-ratio inspirals (EMRIs) are expected to have considerable eccentricity when emitting gravitational waves (GWs) in the LISA band. Developing GW templates that remain phase accurate over these long inspirals requires the use of second-order self-force theory and practical second-order self-force calculations are now emerging for quasi-circular EMRIs. These calculations rely on effective-source regularization techniques in the frequency domain that presently are specialized to circular orbits. Here we make a first step towards more generic second-order calculations by extending the frequency domain effective-source approach to eccentric orbits. In order to overcome the slow convergence of the Fourier sum over radial modes, we develop a new extended effective-sources approach which builds upon the method of extended particular solutions. To demonstrate our new computational technique we apply it a toy scalar-field problem which is conceptually similar to the gravitational case.

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Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. High-Post-Newtonian-Order Dynamics Induced by Tail-of-Tail Interactions: The Non-Geodesic Terms

    gr-qc 2026-08 conditional novelty 7.0 of 10

    The authors compute tail-of-tail contributions to the effective-one-body Q potential through p_r^12 and derive new second-order self-force redshift predictions for eccentric binaries.

  2. Approach to the separatrix with eccentric orbits

    gr-qc 2024-12 conditional novelty 7.0 of 10

    The adiabatic inspiral near the separatrix for eccentric orbits is solved analytically, with the Lambert W_{-1} function controlling the late-time decay of the distance to the separatrix.

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