ÃÛÌÒTV

Gravitational waves (GWs) from inspirals of a stellar mass compact object into a supermassive black hole are one of the main targets for future laser interferometer detectors in space. Using the post-Newtonian (PN) approximation in the first order black hole perturbation theory, we derive the secular changes of orbital parameters up to the fourth post-Newtonian (4PN) order for the compact object in slightly eccentric and arbitrarily inclined orbits around the Kerr black hole. We find that the effect of the absorption of GWs by the Kerr black hole appears at 2.5PN beyond the leading order in the secular change of the energy of the compact object and might induce a superradiance, confirming previously known results for circular orbits. We also find that the superradiance might be suppressed if the inclination angle of the orbits from the equatorial plane of the central black hole increases. In addition, we also investigate the accuracy of the 4PN formulae by comparing to numerical results. Finally, we will also discuss convergence properties of the 4PN formulae which involve expansions in terms of a small velocity and a small eccentricity of the compact object.