Analytical solutions of the geodesic equation in the (rotating) black string-(anti-) de sitter spacetime

TL;DR

This paper derives analytical solutions for geodesic equations in rotating black string-(anti-) de Sitter spacetimes, extending previous models by including an extra compact dimension and classifying particle orbits.

Contribution

It introduces analytical solutions for geodesics in black string-(anti-) de Sitter spacetimes, expanding understanding of particle motion in higher-dimensional black hole geometries.

Findings

Analytical solutions expressed via Weierstrass elliptic and Kleinian sigma functions.

Classification of possible orbits based on energy and angular momentum.

Comparison of geodesic behavior with lower-dimensional spacetimes.

Abstract

In this paper we add a compact dimension to Schwarzschild-(anti-) de sitter and Kerr-(anti-) de sitter spacetimes, which describes (rotating) black string-(anti-) de sitter spacetime. We study the geodesic motion of test particles and light rays in this spacetime. We present the analytical solutions of the geodesic equations in terms of Weierstrass elliptic and Kleinian sigma hyperelliptical functions. We also discuss the possible orbits and classify them according to particle's energy and angular momentum. Moreover, the obtained results, are compared to Schwarzschild-(anti-) de sitter and Kerr-(anti-) de sitter spacetimes.