Publikace ÚTF

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. We decomposed the equations in the
orthonormal tetrad based on the timelike vector fixing the spin condition and on the corresponding spin,
while representing the curvature in terms of the Weyl scalars obtained in the Newman-Penrose null tetrad
naturally associated with the orthonormal one; the projections thus obtained did not contain the Weyl
scalars Ψ0 and Ψ4. In the present paper, we choose the interpretation tetrad in a different way, attaching it to
the tangent uμ 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 decomposition of the MPD equation, again supplemented by writing its right-hand side in
terms of the Weyl scalars, is slightly less efficient than in the massive case, because uμ cannot be freely
chosen (in contrast to Vμ) and so the uμ-based tetrad is less flexible. In the second part of this paper, a
similar analysis is performed for massless spinning particles; in particular, a certain intrinsic interpretation
tetrad is again found. The respective decomposition of the MPD equation of motion is considerably simpler
than in the massive case, containing only Ψ1 and Ψ2 scalars and not the cosmological constant. An option
to span the spin-bivector eigenplane, besides the worldline