Geodesics in Generalised Ellis-Bronnikov Spacetime Embedded in Warped 5D Background

TL;DR

This paper analyzes particle trajectories in a five-dimensional warped Ellis-Bronnikov spacetime, revealing how the warp factor influences geodesic behavior and particle localization, with implications for wormhole physics without exotic matter.

Contribution

It provides a detailed analytical and numerical study of geodesics in 5D-WGEB spacetime, highlighting the effects of the warp factor on particle trajectories and localization.

Findings

Existence of trapped trajectories is highly sensitive to initial conditions in 5D.

Warp factor influences particle localization and trajectory types.

Numerical solutions illustrate the effects of wormhole parameters on geodesics.

Abstract

We study the particle trajectories in the recently proposed five dimensional warped (generalized) Ellis-Bronnikov spacetime (5D-WGEB) (which does not require exotic matter) as well as it's four dimensional counterpart (4D-GEB) in detail and conduct a comparative study. Analytical approach provides conditions which determines three types of trajectories (trapped, returning and crossing) for both 4D and 5D spacetimes. Notably in 5D geometry existence of trapped trajectories become highly sensitive to the initial conditions. We have solved the timelike geodesic equations numerically and presented the trajectories graphically along with corresponding geodesic potentials. We thus distinguished the roles of the so-called wormhole parameter and the warping factor regarding their effects on the trajectories and embedding as such. Interestingly, the 5D-WGEB model shows the localization of massive particles around the location of the brane for growing warp factor and runaway trajectories for decaying warp factor.