Extreme mass ratio inspiral of a spinning body into a Kerr black hole: Generic trajectory and waveforms*

Very large mass-ratio binary black hole systems are of interest theoretically, as a clean limit of the two-body problem in general relativity. These systems are expected to radiate low-frequency gravitational waves detectable by planned space-based Laser Interferometer Space Antenna (LISA). At lowest order, the smaller black hole follows a geodesic of the larger black hole's spacetime. Accurate models of large mass-ratio systems must include post-geodesic corrections, which account for forces driving the small body away from the geodesic. An important post-geodesic effect is gravitational self-force, which describes the small body's interaction with its own spacetime curvature. This effect includes the backreaction due to gravitational-wave emission that leads to the inspiral of the small body into the black hole. When a spinning body orbits a black hole, its spin couples to the curvature of the background spacetime. This introduces another post-geodesic correction called the spin-curvature force. We use osculating element integration to generate a spinning-body inspiral that includes both the backreaction due to gravitational waves and spin-curvature forces. We apply a near-identity (averaging) transformation which eliminates dependence on the orbital phases, allowing for very fast computation of completely generic worldlines of spinning bodies. Finally, we calculate the gravitational waveforms and examine the dephasing of the waveform due to the presence of spin-curvature forces.