Stability of circular orbits of spinning particles in Schwarzschild-like space-times

TL;DR

This paper analyzes the stability of circular orbits of spinning particles in Schwarzschild-like space-times, finding that such orbits are generally stable against radial and normal perturbations, with explicit results for Schwarzschild and de Sitter backgrounds.

Contribution

It provides a detailed stability analysis of spinning particle orbits in Schwarzschild-like backgrounds, including explicit criteria and solutions for perturbations.

Findings

Orbits are stable in de Sitter space.

Orbits are stable in Schwarzschild space.

Stability criteria for normal perturbations are derived.

Abstract

Circular orbits of spinning test particles and their stability in Schwarzschild-like backgrounds are investigated. For these space-times the equations of motion admit solutions representing circular orbits with particles spins being constant and normal to the plane of orbits. For the de Sitter background the orbits are always stable with particle velocity and momentum being co-linear along them. The world-line deviation equations for particles of the same spin-to-mass ratios are solved and the resulting deviation vectors are used to study the stability of orbits. It is shown that the orbits are stable against radial perturbations. The general criterion for stability against normal perturbations is obtained. Explicit calculations are performed in the case of the Schwarzschild space-time leading to the conclusion that the orbits are stable.