Study of the geodesic equations of a spherical symmetric spacetime in conformal gravity

TL;DR

This paper derives analytic solutions for geodesic equations in a spherical conformal spacetime, characterizing orbits and light deflection using special functions, conserved quantities, and effective potentials.

Contribution

It provides explicit analytic solutions for geodesics in spherical conformal gravity using Weierstrass and Kleinian functions, enhancing understanding of particle and light trajectories.

Findings

Analytic solutions expressed via Weierstrass and Kleinian functions

Classification of orbits using conserved energy and angular momentum

Investigation of light deflection in the conformal spacetime

Abstract

Set of analytic solutions of the geodesic equation in a spherical conformal spacetime is presented. Solutions of this geodesics can be expressed in terms of the Weierstrass {\wp} function and the Kleinian {\sigma} function. Using conserved energy and angular momentum we can characterize the different orbits. Also, considering parametric diagrams and effective potentials, we plot some possible orbits. Moreover, with the help of analytical solutions, we investigate the light deflection for such an escape orbit.