Geodesic Properties and Orbits in 5-dimensional Hypercylindrical Spacetime

TL;DR

This paper analyzes geodesic motions of particles and light in a 5D hypercylindrical spacetime, revealing conditions for stable orbits, and calculating light deflection and capture cross sections.

Contribution

It introduces a detailed study of geodesic properties in 5D hypercylindrical spacetime, highlighting the dependence on a key parameter and identifying stability conditions.

Findings

Unstable null geodesic orbits exist only in certain parameter ranges.

Innermost stable circular orbits are present only within specific a ranges.

Light deflection and capture cross sections are quantitatively determined.

Abstract

We investigate the geodesic motions of a massive particle and light ray in the hyperplane orthogonal to the symmetry axis in the 5-dimensional hypercylindrical spacetime. The class of the solutions depends on one constant a which is the ratio of string mass density and tension. There exist unstable orbits in null geodesic only in some range of a. The innermost stable circular orbits in timelike geodesic also exist only in a certain range of the parameter a. The capture cross section and the deflection angle of light ray are also computed.