Mathisson-Papapetrou-Tulczyjew-Dixon (MPTD) equations in ultra-relativistic regime and gravimagnetic moment

MPTD-equations in the Lagrangian formulation correspond to the minimal interaction of spin with gravity. Due to the interaction, in the Lagrangian equations instead of the original metric \(g\) emerges spin-dependent effective metric \(G=g+h(S)\). So we need to decide, which of them the MPTD-particle sees as the space-time metric. We show that MPTD-equations, if considered with respect to original metric, have no physically admissible solutions: acceleration of the particle grows up to infinity as its speed approximates to the speed of light. If considered with respect to \(G\), the theory is consistent. But the metric now depends on spin, so there is no unique space-time manifold for the Universe of spinning particles: each particle probes his own three-dimensional geometry. This can be improved by adding a non-minimal interaction, and gives the modified MPTD-equations with reasonable behavior within the original metric.