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A note on the conversion of orbital angles for extreme mass ratio inspirals

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arxiv 2411.04955 v2 pith:3MXRDKDI submitted 2024-11-07 gr-qc

Philip Lynch , Ollie Burke This is my paper · ORCID
classification gr-qc
keywords anglestimeaction-anglesboyer-lindquistinspiralsquasi-kepleriansourceaction
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We outline a practical scheme for converting between three commonly used sets of phases to describe the trajectories of extreme mass ratio inspirals; quasi-Keplerian angles, Mino time action-angles, and Boyer-Lindquist time action-angles (as utilised by the FastEMRIWaveform package). Conversion between Boyer-Lindquist time action angles and quasi-Keplerian angles is essential for the construction of a source frame for adiabatic inspirals that can be related to the source frames used by other gravitational wave source modelling techniques. While converting from quasi-Keplerian angles to Boyer-Lindquist time action angles via Mino time action-angles can be done analytically, the same does not hold for the converse, and so we make use of an efficient numerical root-finding method. We demonstrate the efficacy of our scheme by comparing two calculations for an eccentric and inclined geodesic orbit in Kerr spacetime using two different sets of orbital angles. We have made our implementations available in Mathematica, C, and Python.

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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. Post-adiabatic dynamics and waveform generation in self-force theory: an invariant pseudo-Hamiltonian framework

    gr-qc 2025-07 conditional novelty 7.0 of 10

    A pseudo-Hamiltonian reformulation of 1PA self-force dynamics yields local, invariant action-angle evolution equations and an embedded conservative Hamiltonian whose on-shell energy equals the first-law binding energy.

  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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