Dynamics of test particles in the five-dimensional, charged, rotating EMCS spacetime

TL;DR

This paper derives and analyzes the geodesic equations for test particles in a five-dimensional charged rotating black hole spacetime, providing analytical solutions and visualizations of particle trajectories.

Contribution

It presents the complete set of geodesic equations and their analytical solutions in terms of elliptic functions for this specific five-dimensional black hole spacetime.

Findings

Analytical solutions for geodesics are expressed using Weierstra{}ss elliptic functions.

Qualitative analysis of particle motion via effective potentials.

Visualization of test particle trajectories in various parameter regimes.

Abstract

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