Antigravity: Spin-gravity coupling in action

The typical motions of a spinning test particle in Schwarzschild’s background which show the strong repulsive action of the highly relativistic spin-gravity coupling are considered using the exact Mathisson-Papapetrou equations. An approximated approach to choice solutions of these equations which describe motions of the particle’s proper center of mass is developed.

Figure 1

Energy vs radial coordinate for the circular orbits of a spinning particle (solid line) and for the geodesic motions (dotted line) with the same initial velocity. The three pictures correspond to the different intervals and scaling by $r$.

Figure 2

Angular momentum vs radial coordinate for the circular orbits of a spinning particle (solid line) and for the geodesic motions (dotted line) with the same initial velocity. The three pictures correspond to the different intervals and scaling by $r$.

Figure 3

Noncircular trajectories of the spinning particle at different initial values of $y_7$. The circle $y_1=2$ corresponds to the horizon line.

Figure 4

An example of the oscillatory motions in the polar coordinates and in the dependence $r$ vs $t$.