Extreme mass-ratio inspiral and waveforms for a spinning body into a Kerr black hole via osculating geodesics and near-identity transformations

Understanding the orbits of spinning bodies in curved spacetime is important for modeling binary black hole systems with small mass ratios. At zeroth order in mass ratio and ignoring its size, the smaller body moves on a geodesic of the larger body's spacetime. Postgeodesic effects, driving motion away from geodesics, are needed to model the system accurately. One very important postgeodesic effect is the gravitational self-force, which describes the small body's interaction with its own contribution to a binary's spacetime. The self-force includes the backreaction of gravitational-wave emission driving inspiral. Another postgeodesic effect, the ``spin-curvature force,'' is due to the smaller body's spin coupling to spacetime curvature. In this paper, we combine the leading orbit-averaged backreaction of point-particle gravitational-wave emission with the spin-curvature force to construct the worldline and associated gravitational waveform for a spinning body spiraling into a Kerr black hole. We use an osculating geodesic integrator, which treats the worldline as evolution through a sequence of geodesic orbits, as well as near-identity (averaging) transformations, which eliminate dependence on orbital phases, allowing for very fast computation of generic spinning-body inspirals. The resulting inspirals and waveforms include all critical dynamical effects which govern such systems (orbit and precession frequencies, inspiral, strong-field gravitational-wave amplitudes), and as such form an effective first model for the inspiral of spinning bodies into Kerr black holes. We emphasize that our present calculation is not self-consistent, since we neglect effects which enter at the same order as effects we include. However, our analysis demonstrates that the impact of spin-curvature forces can be incorporated into extreme mass-ratio inspiral waveform tools with relative ease, making it possible to augment these models with this important aspect of source physics. The calculation is sufficiently modular that it should not be difficult to include neglected postgeodesic effects as efficient tools for computing them become available.