Spinning particles in vacuum spacetimes of different curvature types: Natural reference tetrads and massless particles

In a previous paper, we considered the motion of massive spinning test particles in the "pole-dipole" approximation, as described by the Mathisson-Papapetrou-Dixon (MPD) equations and examined its properties in dependence on the spin supplementary condition. In the present paper, we choose the interpretation tetrad in a different way, attaching it to the tangent u mu of the worldline representing the history of the spinning body. Actually two tetrads are suggested, both given "intrinsically" by the problem and each of them incompatible with one specific spin condition. The respective decomposition of the MPD equation of motion is considerably simpler than in the massive case, containing only [psi]1 and [psi]2 scalars and not the cosmological constant. An option to span the spin-bivector eigenplane, besides the worldline null tangent, by a main principal null direction of the Weyl tensor can lead to an even simpler result.