Eur. Phys. J. C (2015) 75: 346
https://doi.org/10.1140/epjc/s10052-015-3564-9

Regular Article - Theoretical Physics

Kinematic quantities and Raychaudhuri equations in a 5D universe

Department of Mathematics, Kuwait University, P.O. Box 5969, 13060, Safat, Kuwait

^* e-mail: aurel.bejancu@ku.edu.kw

Received: 6 June 2015
Accepted: 9 July 2015
Published online: 28 July 2015

Abstract

Based on some ideas that have emerged from the classical Kaluza–Klein theory, we present a 5D universe as a product bundle over the 4D spacetime. This enables us to introduce and study two categories of kinematic quantities (expansions, shear, vorticity) in a 5D universe. One category is related to the fourth dimension (time), and the other one comes from the assumption of the existence of the fifth dimension. The Raychaudhuri type equations that we obtain in the paper, lead us to results on the evolution of both the 4D expansion and the 5D expansion in a 5D universe.