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

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 (QK) angles, Mino time (MT) action-angles, and Boyer–Lindquist (BL) time action-angles (as utilised by the FastEMRIWaveform package). Conversion between BL time action angles (AAs) and QK 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 QK angles to BL time AAs via MT 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.