Extreme mass-ratio inspiral of a spinning body into a Kerr black hole I: Evolution along generic trajectories

TL;DR

This paper develops a method to model the inspiral of a spinning body into a Kerr black hole by combining gravitational self-force effects and spin-curvature forces, providing a foundation for more accurate waveform predictions.

Contribution

It introduces an osculating geodesic integrator that incorporates both gravitational wave backreaction and spin-curvature forces for spinning bodies in Kerr spacetime.

Findings

Successfully models generic inspirals of spinning bodies.

Includes leading order spin-curvature and gravitational-wave backreaction effects.

Provides groundwork for incorporating secondary spin in waveform models.

Abstract

The study of spinning bodies moving in curved spacetime has relevance to binary black hole systems with large mass ratios, as well as being of formal interest. At zeroth order in a binary's mass ratio, the smaller body moves on a geodesic of the larger body's spacetime. Post-geodesic corrections describing forces driving the small body's worldline away from geodesics must be incorporated to model the system accurately. An important post-geodesic effect is the 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 spacetime curvature. This introduces another post-geodesic correction known as the spin-curvature force. An osculating geodesic integrator that includes both the backreaction due to gravitational waves and spin-curvature forces can be used to generate a spinning-body inspiral. In this paper, we use an osculating geodesic integrator to combine the leading backreaction of gravitational waves with the spin-curvature force. Our analysis only includes the leading orbit-averaged dissipative backreaction, and examines the spin-curvature force to leading order in the small body's spin. This is sufficient to build generic inspirals of spinning bodies, and serves as a foundation for further work examining how to include secondary spin in large-mass-ratio waveform models.