LAUSR

In 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 Mathission-Papapetrau's 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 $S^{a} = \left(0,S^r,S^{\theta},0\right)$ , there exists an unique circular orbit at $(r_c,\theta_c)$ 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 non-equatorial plane. We further establish that the location ($r_c,\theta_c$) of the ISCO for a given spinning particle depends on the radial component of the spin vector ($S^r$) as well as the angular momentum of the black hole ($J$). The implications of using different spin supplementary conditions are investigated.