The Ricci Rotation Coefficients in the Description of Trajectories of Spinning Test Particles Off-equatorial Plane in the Gravitational Field of a Rotating Source

We describe the trajectories of circular orbits of spinless and spinning test particles around a rotating body in equatorial and non-equatorial planes via the Mathisson-Papapetrou-Dixon equations. In this paper, these equations include the Ricci rotation coefficients with the purpose of describing not only the curvature of space time, but also the rotation of the spinning test particles that orbit around a rotating massive body. We found a numerical difference between the trajectories of spinless test particles and spinning test particles in the order of \({\varvec{10}}^{\varvec{-7}}\) ${\mathbf{10}}^{\mathbf{-}\mathbf{7}}$ . We take as parameters: radius, energy, Carter’s constant and angular momentum.