The next-to-leading spin-orbit effects on the general motions in Kerr spacetime

Abstract

We derive the second-and-half post-Newtonian solutions for the generally inclined motion of a test particle in Kerr spacetime when the effects of the spin-induced quadrupole are negligible. The next-to-leading order spin-orbit effects on the test particle's motion are obtained, which are important in fitting the motions of the extremely-mass-ratio-inspiral systems and also calculating the gravitational wave radiated by this kind of systems at the second-and-half post-Newtonian order.