Detailed study of geodesics in the Kerr-Newman-(A)dS spactime and the rotating charged black hole spacetime in $f(R)$ gravity

TL;DR

This paper provides a comprehensive analysis of geodesic equations in Kerr-Newman-(A)dS and $f(R)$ gravity black hole spacetimes, deriving solutions and classifying orbit types using advanced mathematical functions.

Contribution

It derives explicit solutions for geodesics in these complex spacetimes and analyzes their motion, including the impact of $f(R)$ gravity modifications.

Findings

Explicit solutions for geodesics using Weierstrass and Kleinian functions

Classification of orbit types via parametric diagrams and potentials

Insight into particle and light ray trajectories in charged, rotating black holes

Abstract

We perform a detailed study of the geodesic equations in the spacetime of the static and rotating charged black hole corresponding to the Kerr-Newman-(A)dS spacetime. We derive the equations of motion for test particles and light rays and present their solutions in terms of the Weierstrass $\wp$, $\zeta$ and $\sigma$ functions as well as the Kleinian $\sigma$ function. With the help of parametric diagrams and effective potentials we analyze the geodesic motion and classify the possible orbit types. This spacetime is also a solution of $f(R)$ gravity with a constant curvature scalar.