Geodesic Congruences in 5D Warped Ellis-Bronnikov Spacetimes

TL;DR

This paper investigates the behavior of timelike geodesic congruences in 4D and 5D warped Ellis-Bronnikov spacetimes, revealing how wormhole parameters and warp factors influence geodesic evolution and congruence rotation.

Contribution

It provides analytical and numerical analysis of geodesic congruences in 4D-GEB and 5D-WGEB spacetimes, highlighting the effects of wormhole parameters and warping on geodesic dynamics.

Findings

Warping factors induce rotation or accretion in geodesic congruences.

Wormhole parameters significantly affect geodesic evolution.

Rotation in congruences plays a crucial role in spacetime dynamics.

Abstract

We study the timelike geodesic congruences in the generalized Ellis-Bronnikov spacetime (4D-GEB) and in recently proposed 5D model where a 4D-GEB is embedded in a warped geometry (5D-WGEB) and conduct a comparative study. Analytical expressions of ESR variables (for 4D geometries) are found which reveal the role of the wormhole parameter. In more general 4D and 5D scenarios geodesic equation, geodesic deviation equation and Raychaudhury equations are solved numerically. The evolution of cross-sectional area of the congruences of timelike geodesics (orthogonal to the geodesic flow lines) projected on 2D-surfaces yield an interesting perspective and shows the effects of the wormhole parameter and growing/decaying warp factors. Presence of warping factor triggers rotation or accretion even in the absence of initial congruence rotation. Presence of rotation in the congruence is also found to be playing a crucial role which we discuss in detail.