Equations of Motion of Spinning Relativistic Particle in Electromagnetic and Gravitational Fields

TL;DR

This paper derives equations of motion for a relativistic spinning particle in electromagnetic and gravitational fields, emphasizing the importance of a noncovariant spin formalism and exploring effects like gravimagnetic moments and spin interactions.

Contribution

It introduces a noncovariant spin formalism for accurate trajectory description and provides new equations of motion that differ from Papapetrou's, including detailed calculations up to second order in spin.

Findings

The true coordinate of a spinning particle is its naive coordinate.

Derived gravitational spin-orbit and spin-spin interactions.

Found that the gravimagnetic ratio for Kerr black holes equals one.

Abstract

We consider the motion of a spinning relativistic particle in external electromagnetic and gravitational fields, to first order in the external field, but to an arbitrary order in spin. The noncovariant spin formalism is crucial for the correct description of the influence of the spin on the particle trajectory. We show that the true coordinate of a relativistic spinning particle is its naive, common coordinate $\r$. Concrete calculations are performed up to second order in spin included. A simple derivation is presented for the gravitational spin-orbit and spin-spin interactions of a relativistic particle. We discuss the gravimagnetic moment (GM), a specific spin effect in general relativity. It is shown that for the Kerr black hole the gravimagnetic ratio, i.e., the coefficient at the GM, equals unity (just as for the charged Kerr hole the gyromagnetic ratio equals two). The equations of motion obtained for relativistic spinning particle in external gravitational field differ essentially from the Papapetrou equations.