Particle motion in the field of a five-dimensional charged black hole

TL;DR

This paper analyzes the motion of neutral particles around a five-dimensional charged black hole, focusing on geodesics, stability of orbits, and the differences between massive particles and photons using effective potential and dynamical systems methods.

Contribution

It introduces a comparative approach to study geodesics in five-dimensional charged black holes, including stability analysis and orbit characterization, which is novel in higher-dimensional black hole research.

Findings

Photons have only two possible circular orbit radii.

Multiple stable and unstable orbits exist for massive particles.

Dynamical systems analysis reveals critical points and trajectory behaviors.

Abstract

In this paper, we have investigated the geodesics of neutral particles near a five-dimensional charged black hole using a comparative approach. The effective potential method is used to determine the location of the horizons and to study radial and circular trajectories. This also helps us to analyze the stability of radial and circular orbits. The radius of the innermost stable circular orbits have also been determined. Contrary to the case of massive particles for which, the circular orbits may have up to eight possible values of specific radius, we find that the photons will only have two distinct values for the specific radii of circular trajectories. Finally we have used the dynamical systems analysis to determine the critical points and the nature of the trajectories for the timelike and null geodesics.