Geodesic motion in the spacetime of a static charged black hole in $f(R)$ gravity

TL;DR

This paper analytically solves the geodesic equations for particles and light in the spacetime of a static charged black hole within $f(R)$ gravity, classifying possible orbits using elliptic functions and effective potentials.

Contribution

It provides the first complete analytic solutions of geodesic equations in this specific $f(R)$ black hole spacetime, including orbit classification.

Findings

Analytic solutions expressed via Weierstrass and Kleinian functions.

Classification of orbit types based on conserved quantities.

Analysis of geodesic motion using effective potentials.

Abstract

In the present paper we study the geodesic motion of test particles and light rays in the spacetime of a static charged black hole in $f(R)$ gravity. The complete set of analytic solutions of the geodesic equations in the spacetime of this black hole are presented. The geodesic equations are solved in terms of Weierstrass elliptic $\wp$ function and derivatives of Kleinian $\sigma$ function. With the help of parametric diagrams and effective potentials we analyze the geodesic motion and give a list of all possible orbit types. The different types of the resulting orbits are characterized in terms of the conserved energy, angular momentum, charge and cosmological constant.