Alexei A Deriglazov
Universidade Federal de Juiz de Fora, Brazil
Posters & Accepted Abstracts: J Phys Chem Biophys
Mathisson-Papapetrou-Tulczyjew-Dixon (MPTD) equations are widely assumed during the seventy years as the basic tool for description of a rotating body in general relativity. We propose the Lagrangian formulation of MPTD equations and analyze them on this base. We show that MPTD equations 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 ultrarelativistic limit. If considered with respect to G, the theory has no such 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 its 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.
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