2015/09/30 by Alexei A. Deriglazov, Walberto Guzmán Ramírez · 1 citation
Mathematics · Physics and Astronomy · #gr-qc #hep-th #math-ph #math.MP
paper · pdf · doi:10.1142/s021827181750047x
published as International Journal of Modern Physics D Vol. 26 (2017) 1750047 (12 pages) · 5 pages, typos corrected, close to published version
arxiv created 2016/10/13 · arxiv updated 2016/11/10
Mathisson-Papapetrou-Tulczyjew-Dixon (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 unsatisfactory behavior: the acceleration in the direction of velocity grows up to infinity in the ultra-relativistic limit. If considered with respect to G, the theory has no this problem. 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 of spin with gravity through gravimagnetic moment. The modified MPTD equations with unit gravimagnetic moment have reasonable behavior within the original metric.