Geodesic motion in the (rotating) black string spacetime

TL;DR

This paper analyzes the geodesic motion of particles and light in five-dimensional rotating black string spacetimes, revealing new behaviors introduced by the extra compact dimension and providing analytical solutions.

Contribution

It presents the first analytical solutions of geodesic equations in five-dimensional rotating black string spacetimes, highlighting differences from four-dimensional cases.

Findings

New geodesic behaviors due to the extra dimension

Analytical solutions for geodesic equations

Comparison of orbits in 4D and 5D spacetimes

Abstract

In this article we study the geodesic motion of test particles and light in the five-dimensional (rotating) black string spacetime. If a compact dimension is added to the four-dimensional Schwarzschild or Kerr spacetime, the new five-dimensional metric describes a (rotating) black string. The geodesics in the Schwarzschild and Kerr spacetime have been studied in great detail, however, when a compact dimension is added new behaviour occurs. We present the analytical solutions of the geodesic equations and discuss the possible orbits. The motion in the ordinary four-dimensional Schwarzschild and Kerr spacetime is compared to the motion in the (rotating) black string spacetime.