Dynamics of test bodies with spin in de Sitter spacetime

TL;DR

This paper investigates the motion of spinning test bodies in de Sitter spacetime, deriving explicit expressions for momentum and spin, and analyzing their trajectories under different supplementary conditions.

Contribution

It provides explicit formulas for momentum and spin in de Sitter spacetime and examines the dynamics under Frenkel and Tulczyjew conditions.

Findings

Explicit expressions for 4-momentum and spin tensor derived.

Trajectories depend on the supplementary condition imposed.

Analysis of spinning body dynamics in a curved spacetime context.

Abstract

We study the motion of spinning test bodies in the de Sitter spacetime of constant positive curvature. With the help of the 10 Killing vectors, we derive the 4-momentum and the tensor of spin explicitly in terms of the spacetime coordinates. However, in order to find the actual trajectories, one needs to impose the so-called supplementary condition. We discuss the dynamics of spinning test bodies for the cases of the Frenkel and Tulczyjew conditions.