Dynamics of spinning test bodies in the Schwarzschild space-time: reduction and circular orbits

TL;DR

This paper analyzes the motion of spinning test bodies in Schwarzschild space-time, reducing the problem to a Hamiltonian system, identifying new circular orbits, and studying bifurcations of periodic solutions.

Contribution

It introduces a reduction of the spinning body problem to a three-degree-of-freedom Hamiltonian system and discovers new circular orbits with unique angular momentum properties.

Findings

New circular orbits with non-parallel angular momentum

Bifurcation analysis of periodic solutions

Reduction to a three-degree-of-freedom Hamiltonian system

Abstract

This paper investigates the motion of a rotating test body in the Schwarzschild space-time. After reduction, this problem reduces to an analysis of a three-degree-of-freedom. Hamiltonian system whose desired trajectories lie on the invariant manifold described by the Tulczyjew condition. An analysis is made of the fixed points of this system which describe the motion of the test body in a circle. New circular orbits are found for which the orbital angular momentum is not parallel to the angular momentum of the test body. Using a Poincare map, bifurcations of periodic solutions are analyzed.