Quadrupole effects on the motion of extended bodies in Kerr spacetime

The motion of a body endowed with dipolar as well as quadrupolar structure is investigated in the Kerr background according to the Dixon's model, extending a previous analysis done in the Schwarzschild background. The full set of evolution equations is solved under the simplifying assumptions of constant frame components for both the spin and the quadrupole tensors and that the center of mass moves along an equatorial circular orbit, the total four-momentum of the body being aligned with it. We find that the motion deviates from the geodesic one due to the internal structure of the body, leading to measurable effects. Corrections to the geodesic value of the orbital period of a close binary system orbiting the Galactic Center are discussed assuming that the Galactic Center is a Kerr supermassive black hole.