• black hole physics;
  • gravitation;
  • relativity


The motion of small spinning free test bodies is usually treated within the ‘pole–dipole’ approximation, which – in general relativity – leads to Mathisson–Papapetrou (MP) equations. These have to be supplemented by three side constraints in order to provide a unique solution. Several different ‘spin conditions’ have been proposed and used in the literature, each leading to different worldlines. In a previous paper, we integrated the MP equations with the pσSμσ= 0 condition numerically in Kerr space–time and illustrated the effect of the spin–curvature interaction by comparing the trajectories obtained for various spin magnitudes. Here we also consider other spin conditions and clarify their interrelations analytically as well as numerically on particular trajectories. The notion of a ‘minimal worldtube’ is introduced in order to judge the individual supplementary conditions and to expose the limitations of the pole–dipole approximation.