A new approach to the calculation of extreme-mass-ratio inspirals with a spinning secondary

TL;DR

This paper presents a new, efficient framework for modeling gravitational waves from eccentric, spinning EMRIs, incorporating secondary spin effects to improve accuracy for future space-based GW detectors.

Contribution

It introduces a practical method to include secondary spin effects in EMRI models using analytic solutions and flux-balance laws, enhancing waveform accuracy.

Findings

Framework accurately models spin-induced phase shifts.

Method simplifies calculations using analytic solutions.

Code implementation is publicly available in KerrSpinningFluxes.

Abstract

Extreme-mass-ratio inspirals (EMRIs) are among the most promising sources for future space-based gravitational-wave (GW) detectors, such as LISA. To fully leverage the scientific potential, the GW templates required for parameter estimation must be modeled with high accuracy for eccentric precessing binary systems with nonzero spins. This work introduces a practical and efficient framework for incorporating the effects of secondary spin in fully generic, eccentric, and offequatorial EMRIs to the first postadiabatic order. We utilize recently found analytic solutions for the trajectories of spinning bodies in Kerr spacetime to significantly simplify the calculation of the corresponding asymptotic GW fluxes. Furthermore, thanks to the recently proven flux-balance laws, we show how to express the rates of change of the constants of motion, including the Carter-R\"udiger constant, using asymptotic Teukolsky amplitudes and purely geodesic functions that are already established in the literature. Finally, we show how this framework performs in the case of nearly-spherical inspirals and demonstrate that the resulting spin-induced phase shifts are gauge independent. A Wolfram Mathematica implementation of the code developed in this work is publicly available in the KerrSpinningFluxes package.