Tilted Circular Orbits around a Kerr Black Hole

Abstract

We study circular orbits that are tilted with respect to the equatorial plane around a Kerr black hole. We write the equations for the parameters of a tilted circular orbit in terms of the orbit's radius and the Carter constant, or equivalently, the tilt angle. The tilted innermost stable circular orbits (TISCO)s are discussed as well as the last circular orbits. The azimuthal precession of an orbit is then studied and an approximate expression for the precession speed is given. We finally try to link tilted circular orbits to quai-periodic oscillations in some astrophysical black hole systems.