Geodesic Motion in the Spacetime Of a SU(2)-Colored (A)dS Black Hole in Conformal Gravity

TL;DR

This paper analyzes the paths of particles and light around a specific black hole in conformal gravity, deriving analytical solutions and classifying orbit types based on energy and angular momentum.

Contribution

It provides the first analytical solutions for geodesic equations in SU(2)-colored (A)dS black hole spacetime within conformal gravity.

Findings

Analytical solutions for geodesic equations using elliptic functions

Classification of orbit types based on energy and angular momentum

Illustrative examples of possible particle and light trajectories

Abstract

In this paper, we study the geodesic motion in the spacetime of a SU(2)-colored (A)dS black hole in conformal gravity, and also we investigate spacetime features, such as light spheres and horizons. Moreover, we derive the analytical solutions for the equation of motion of test particles and light rays using Weierstrass elliptic and Kleinian sigma functions. Depending on the particle energy levels and angular momentums, we classify the solutions of the geodesic equations. Furthermore, several examples of possible types of orbits illustrate the results