Classical defocussing of world lines in higher dimensions

A five-dimensional gravity theory, motivated by the brane-world picture, with Kaluza scalar in the 5-dimensional metric as g55(r);r=x2+y2+z2, is considered near the possible singularity (small distance scales where gravity is strong) and is shown to give rise to a positive contribution to the Raychaudhuri equation. This inhibits the focusing of world lines and contributes to non-focusing of the worldlines in the 5-dimensional space. It is also shown that the results extend to time dependent cases such as those relevant for black hole interiors and cosmology.