Equations for spinning test particles in equatorial orbits when they are orbiting in a weak rotating field

TL;DR

This paper derives equations for spinning test particles in circular equatorial orbits within a weak Kerr gravitational field, providing insights into spin effects in rotating spacetime relevant to gravitomagnetism and gravitational waves.

Contribution

It formulates the equations of motion for spinning particles in a weak Kerr metric and compares spinless and spinning cases for circular orbits.

Findings

Equations for spinning particles in weak Kerr fields are derived.

Results compare spin effects in circular orbits.

Guidelines for studying spin influence in gravitational phenomena.

Abstract

This paper formulates, via the Mathisson - Papapetrou - Dixon equations, the system of equations for a test particle with spin when it is orbiting a weak Kerr metric. We shall restrict ourselves to the case of circular orbits with the purpose of comparing our results with the results of the literature. In particular, we solve the set of equations of motion for the case of circular trajectories both spinless and spinning test particles around rotating bodies in equatorial plane. The results obtained are an important guideline for the study of the effects of the particles with spin in rotating gravitational fields such as Gravitomagnetics Effects or gravitational waves.