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

Abstract

We derive the second-and-half post-Newtonian solution 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.

The second post-Newtonian motion in Reissner-Nordström spacetime

“…When taking the limit of extreme mass ratio, the solutions for the motion of the binary systems return to the solution of the motion of the test particle. Based on these studies, we have achieved the analytical solutions for the motion of the test particle under the most generally parameterized PN force [24,25], and those in the spacetime of the classical black holes, including the 2PN effects of the mass in the Wagoner-Will-Epstein-Haugan representation [26], the 2PN effects of the spin-induced quadrupole on the equatorial motion in Kerr spacetime [27] and the 2.5PN effects of the spin-orbit coupling on the general motion in the Kerr spacetime [28].…”

The quasi-Keplerian motion in the regular Bardeen spacetime

“…We obtained the effects of the spin-induced quadrupole on the equatorial motion of a test particle in the Kerr spacetime [59] and the next-to-leading order spin-orbit effects on the test particle's generally inclined motion [60]. In this work, we will derive the quasi-Keplerian motion of a test particle in the gravitational field of regular Bardeen black hole under the standard spherical coordinates.…”