Relativistic effects due to gravimagnetic moment of a rotating body

TL;DR

This paper derives exact Hamiltonian formulations for spinning particles with gravimagnetic moments in gravitational fields, revealing significant differences in behavior and frame-dragging effects compared to traditional models.

Contribution

It introduces a modified set of equations for spinning bodies with gravimagnetic moments, providing exact Hamiltonian and Dirac brackets applicable in arbitrary gravitational backgrounds.

Findings

Rotating bodies with gravimagnetic moment exhibit different precession behavior.

Gravimagnetic moments contribute significantly to frame-dragging effects.

Modified equations behave well in the ultrarelativistic limit.

Abstract

We compute exact Hamiltonian (and corresponding Dirac brackets) for spinning particle with gravimagnetic moment $\kappa$ in an arbitrary gravitational background. $\kappa=0$ corresponds to the Mathisson-Papapetrou-Tulczyjew-Dixon (MPTD) equations. $\kappa=1$ leads to modified MPTD equations with reasonable behavior in the ultrarelativistic limit. So we study the modified equations in the leading post-Newtonian approximation. Rotating body with unit gravimagnetic moment has qualitatively different behavior as compared with MPTD body: A) If a number of gyroscopes with various rotation axes are freely traveling together, the angles between the axes change with time. B) For specific binary systems, gravimagnetic moment gives a contribution to frame-dragging effect with the magnitude, that turns out to be comparable with that of Schiff frame dragging.