Spinning particles in NUT-Reissner-Nordström space-time (Q5952990)

In this paper, the authors investigate the geodesic motion of pseudo-classical spinning particles in the NUT-Reissner-Nordström spacetime and several nice results are found, which according to the authors may be interesting in the study of gravitational instantons as well as in long rang-range monopole dynamics. By pseudo classical they understand a particle described by a timelike curve on the world manifold, with a set of four Grassmann coordinates defined on the timelike curve. This approach has been used in equivalent ways by several other authors in similar (but not equivalent) problems. We may wonder what are the geometrical meaning of Grassmann variables on the model. The answer is that all these theories can be easily translated in a theory of \textit{Frenet curves} on a Lorentzian manifold. If, moreover, a Clifford calculus is used to present the theory of Frenet curves, spin appears immediately as associated with a part of the Darboux bivector [associated with extra rotation (in spacetime) than the one described by the Fermi-Walker connection] and it is seen to be related to the Pauli-Lubanski (spin) vector. Also, multivector Lagrangians can be introduced, in particular given an obvious interpretation to the famous Berezin-Marinov paper [\textit{F. A. Berezin} and \textit{M. S. Marinov}, Ann. Phys. 104, 336-362 (1977; Zbl 0354.70003)] on the dynamics of the superparticle. These ideas have been developed in [\textit{W. A. Rodrigues} jun., \textit{J. Vaz} jun. and \textit{M. Pavsic}, Banach Cent. Publ. 37, 295-314 (1996; Zbl 1010.81507)].