Mathisson Equations: Non-Oscillatory Solutions in a Schwarzschild Field

TL;DR

This paper investigates the Mathisson equations for spinning particles in a Schwarzschild field, focusing on non-oscillatory solutions relevant for astrophysical scenarios involving relativistic motions and gravitational spin-orbit effects.

Contribution

It introduces a method for selecting non-oscillatory solutions of the Mathisson equations in a Schwarzschild background, especially for highly relativistic motions.

Findings

Identified conditions for non-oscillatory solutions

Proposed a calculation procedure for relativistic motions

Discussed implications for gravitational spin-orbit interactions

Abstract

The Mathisson equations under the Frenkel-Mathisson supplementary condition are studied in a Schwarzschild field. The choice of solutions, which describe the motions of the proper center of mass of a spinning test particle, is discussed, and the calculation procedure for highly relativistic motions is proposed. The very motions are important for astrophysics while investigating possible effects of the gravitational spin-orbit interaction on the particle's world line and trajectory.