Geodesic congruences in 5D warped Ellis–Bronnikov spacetimes

Abstract

We study the timelike geodesic congruences in the generalised 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 Raychaudhuri 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. The presence of warping factor triggers rotation or accretion even in the absence of initial congruence rotation. The presence of rotation in the congruence is also found to be playing a crucial role which we discuss in detail.