Dynamics of test particles in the five-dimensional G\"{o}del spacetime

TL;DR

This paper derives and analyzes the geodesic equations for test particles in a five-dimensional rotating and charged G"{o}del spacetime, providing analytical solutions and visualizations of their motion.

Contribution

It presents the complete set of geodesic equations and their analytical solutions for test particles in a five-dimensional G"{o}del spacetime, including charged particles.

Findings

Characterization of test particle motion via effective potentials

Analytical solutions for geodesic equations

Visualization of particle trajectories in 3D plots

Abstract

We derive the complete set of geodesic equations for massive and massless, charged test particles of a five-dimensional, rotating and charged solution of the Einstein-Maxwell-Chern-Simons field equations in five-dimensional minimal gauged supergravity and present their analytical solutions. We study the polar and radial motion, depending on the spacetime and test particle parameters, and characterize the test particle motion qualitatively by the means of parametric plots and effective potentials. We use the analytical solutions in order to visualize the test particle motion by three-dimensional plots.