Worldine deviations and epicycles

TL;DR

This paper develops a relativistic framework for understanding world line deviations and epicycles, generalizing classical orbital models to include effects of charge and spin in general relativity.

Contribution

It introduces a unified formalism for world line deviations in general relativity, extending to charged and spinning test bodies, and presents a relativistic version of the Ptolemaean epicycle scheme.

Findings

Derived equations for world line deviations including charge and spin effects.

Established a relativistic epicycle model for particle motion in central fields.

Unified geometric and background field approaches to deviations.

Abstract

In general relativity, only relative acceleration has an observer-independend meaning: curvature and non-gravitational forces determine the rate at which world lines of test bodies diverge or converge. We derive the equations governing both in the conventional geometric formalism as well as using the background field method. This allows us to generalize the results to test bodies with charge and/or spin. The application of the equations to the motion of particles in a central field results in an elegant, fully relativistic version of the Ptolemaean epicycle scheme.