Off-equatorial stable circular orbits for spinning particles

TL;DR

This paper studies the existence and properties of stable off-equatorial circular orbits for spinning particles around Kerr black holes, revealing how spin orientation influences orbit stability and location.

Contribution

It demonstrates the existence of unique off-equatorial ISCOs for spinning particles and analyzes how spin and black hole parameters affect their positions.

Findings

Existence of unique off-equatorial ISCOs for spinning particles.

Orbit location depends on spin vector components and black hole angular momentum.

Different spin supplementary conditions influence orbit stability and position.

Abstract

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.