Particle Dynamics Around the Black String

TL;DR

This study explores the dynamics of neutral and charged particles around a five-dimensional black string, analyzing stable orbits, escape velocities, and the influence of extra dimensions on particle motion.

Contribution

It provides the first detailed analysis of particle dynamics around a five-dimensional black string, including the effects of an extra dimension and magnetic fields on orbits and stability.

Findings

Extra dimension slightly influences effective potential and force.

The new constant of motion affects orbit stability and shape.

Differences observed between black hole and black string cases.

Abstract

In this paper, some dynamical properties of neutral and charged particles around a weakly magnetized five-dimensional static black string have been studied. The perturbation method was also used to calculate the Innermost Stable Circular Orbit (ISCO) of this metric in the presence of a magnetic field. The escape velocity of neutral and charged particles around the black string was derived. In the next step, the analytical solutions of the equations of motion were discussed and some possible orbits for particles in the black string space-time were plotted. Interestingly, it was found that adding an extra dimension has a slight influence on the effective potential and one term of the effective force. The magnitude of the new constant of motion $(J)$ affects both the shape of the potential and existence of the stable circular orbits. In conclusion, by comparing a black hole and a black string, it is realized that the value of a new constant of motion causes slight but interesting differences.