Multipole particle in relativity

TL;DR

This paper develops a framework for describing the motion of extended objects in relativity using multipole moments and Lie group classification, deriving equations of motion that generalize the Papapetrou equations.

Contribution

It introduces a new approach to classify multipole moments via Lie group SO(3) and derives simplified equations of motion for extended objects in relativity.

Findings

Reproduces the Papapetrou equations for spinning particles.

Provides simpler equations by adjusting the center-of-mass.

Framework for classifying multipole moments in relativity.

Abstract

We discuss the motion of extended objects in a spacetime by considering a gravitational field created by these objects. We define multipole moments of the objects as a classification by Lie group SO(3). Then, we construct an energy-momentum tensor for the objects and derive equations of motion from it. As a result, we reproduce the Papapetrou equations for a spinning particle. Furthermore, we will show that we can obtain more simple equations than the Papapetrou equations by changing the center-of-mass.