Geodesic congruences in warped spacetimes

Abstract

In this article, we explore the kinematics of timelike geodesic congruences in warped five dimensional bulk spacetimes, with and without thick or thin branes. Beginning with geodesic flows in the Randall--Sundrum AdS (Anti de Sitter) geometry without and with branes we find analytical expressions for the expansion scalar and comment on the effects of including thin branes on its evolution. Later, we move on to congruences in more general warped bulk geometries with a cosmological thick brane and a time-dependent extra dimensional scale. Using analytical expressions for the velocity field, we interpret the expansion, shear and rotation (ESR) along the flows, as functions of the extra dimensional coordinate. The evolution of a cross-sectional area orthogonal to the congruence, as seen from a local observer's point of view, is also shown graphically. Finally, the Raychaudhuri and geodesic equations in backgrounds with a thick brane are solved numerically in order to figure out the role of initial conditions (prescribed on the ESR) and spacetime curvature on the evolution of the ESR.

18 pages, 5 figures, 2 Tables, published version

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• FLRW cosmology in Weyl-Integrable Space-Time
• Geodesic Congruences and Their Deformations in Bertrand Space-times
• Evolution of geodesic congruences in a gravitationally collapsing scalar field background
• Kinematics of trajectories in classical mechanics
• Five-dimensional warped product space-time with time-dependent warping and a scalar field in the bulk
• Standing Waves Braneworlds
• 5D non-symmetric gravity and geodesic confinement