The spherically-symmetrical trajectories of spin particles in the Schwarzschild field

The motion of spin particles in the Schwarzschild field is examined in this paper. It is shown that Mathisson-Papapetrou equations under additional conditions, where is the Lie derivative of the Killing vector _j, permit only radial motion, motion in the equatorial plane and in the equilibrium points. All these types of motion are considered more in detail.