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

TL;DR

This paper investigates the behavior of Mathisson-Papapetrou-Tulczyjew-Dixon (MPTD) equations in the ultra-relativistic regime, showing that incorporating a gravimagnetic moment improves their physical consistency within the original spacetime metric.

Contribution

It introduces a non-minimal spin-gravity interaction via gravimagnetic moment to address ultra-relativistic issues in MPTD equations, ensuring better physical behavior.

Findings

MPTD equations exhibit infinite acceleration in ultra-relativistic limit when using the original metric.

Using a spin-dependent effective metric resolves the acceleration divergence.

Adding gravimagnetic moment yields well-behaved equations in the original metric.

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.