Fluxes of Generic Extreme-Mass-Ratio Inspirals with a Spinning Secondary

Abstract

Extreme mass-ratio inspirals (EMRIs), comprising a stellar-mass compact object (CO) orbiting a supermassive black hole (BH), are key targets for future space-based gravitational-wave (GW) observatories. Incorporating the spin of the secondary body into waveform models not only enhances measurement precision but also offers insight into the spin distribution of stellar-mass objects. In this work, we construct the flux and waveform for an EMRI with a spinning secondary in a Kerr background under the linear-spin approximation. Using the radiative prescription (half-retarded minus half-advanced field), we derive orbit-averaged evolution equations for the fundamental constants of motion, including the energy, angular momentum, Carter-like constant, and the parallel spin component. This framework provides a tractable route to generating waveforms that incorporate the secondary spin, with the potential for further simplification in future work.