Extreme mass ratio inspirals with spinning secondary: A detailed study of equatorial circular motion

Extreme-mass-ratio inspirals (EMRIs) detectable by the future Laser Interferometer Space Antenna provide a unique way to test general relativity and fundamental physics. Motivated by this possibility, here we study in detail the EMRI dynamics in the presence of a spinning secondary, collecting and extending various results that appeared in previous work and also providing useful intermediate steps and new relations for the first time. We present the results of a frequency-domain code that computes gravitational-wave fluxes and the adiabatic orbital evolution for the case of circular, equatorial orbits with (anti)aligned spins. The spin of the secondary starts to affect the gravitational-wave phase at the first post-adiabatic order (as does the first-order conservative self-force) and introduces a detectable dephasing, which can be used to measure it at the 5-25% level, depending on individual spins. In a companion paper we discuss the implication of this effect for tests of the Kerr bound.