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

Abstract

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.

5 pages, typos corrected, close to published version

References in corpus (5)

• Investigating spinning test particles: spin supplementary conditions and the Hamiltonian formalism
• Lagrangian formulation for Mathisson-Papapetrou-Tulczyjew-Dixon (MPTD) equations
• Covariant hamiltonian spin dynamics in curved space-time
• Lagrangian for the Frenkel electron
• World-line geometry probed by fast spinning particle

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