Off-equatorial stable circular orbits for spinning particles

Abstract

n this article, we investigate the motion of a spinning particle at a constant inclination, different from the equatorial plane, around a Kerr black hole. We mainly explore the possibilities of stable circular orbits for different spin supplementary conditions. The Mathisson-Papapetrou equations are extensively applied and solved within the framework of linear spin approximation. We explicitly show that for a given spin vector of the form Sa=(0,Sr,Sθ,0), there exists a unique circular orbit at (rc, θc) defined by the simultaneous minima of energy, angular momentum, and Carter constant. This corresponds to the innermost stable circular orbit (ISCO) which is located on a nonequatorial plane. We further establish that the location (rc, θc) of the ISCO for a given spinning particle depends on the radial component of the spin vector (Sr) as well as the angular momentum of the black hole (J). The implications of using different spin supplementary conditions are investigated.