Exotic orbits due to spin-spin coupling around Kerr black holes

We report exotic orbital phenomena of spinning test particles orbiting around a Kerr black hole, i.e., some orbits of spinning particles are asymmetrical about the equatorial plane. When a nonspinning test particle orbits around a Kerr black hole in a strong field region, due to relativistic orbital precessions, the pattern of trajectories is symmetrical about the equatorial plane of the Kerr black hole. However, the patterns of the spinning particles' orbit are no longer symmetrical about the equatorial plane for some orbital configurations and large spins. We argue that these asymmetrical patterns come from the spin-spin interactions between spinning particles and Kerr black holes, because the directions of spin-spin forces can be arbitrary, and distribute asymmetrically about the equatorial plane.