# Classical Defocussing of world lines from Higher Dimensions

## TL;DR

This paper investigates how a five-dimensional gravity model, inspired by brane-world theories, causes defocusing of world lines near singularities, with implications for black hole interiors and cosmology.

## Contribution

It demonstrates that the Kaluza scalar in a 5D metric leads to non-focusing of world lines, extending to dynamic scenarios like black holes and cosmological models.

## Key findings

- Positive contribution to Raychaudhuri equation inhibits world line focusing
- Results extend to time-dependent black hole and cosmological cases
- Suggests higher-dimensional effects influence singularity behavior

## Abstract

A five-dimensional gravity theory, motivated by the brane-world picture, with Kaluza scalar in the 5 - dimensional metric as $g_{55}(r); r=\sqrt{x^2+y^2+z^2}$, 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.