Raychaudhuri Equation in Kaluza Klein space time

TL;DR

This paper investigates the Raychaudhuri equation within Kaluza-Klein space-time, deriving a new term that influences the behavior of world lines near charged higher-dimensional black hole singularities.

Contribution

It introduces a novel term in the Raychaudhuri equation specific to Kaluza-Klein unification, affecting black hole interior analysis.

Findings

Derived an additional term affecting world line defocus

Modified the understanding of scalar effects on black hole singularities

Proved theorems providing insights into black hole interiors

Abstract

We studied the Raychaudhuri equation in Kaluza-Klein space-time. We derived an additional term that is solely due to Kaluza-Klein's unification. This term affects the defocus of world lines near the singularity of charged higher-dimensional black holes. We illustrated it with a static higher-dimensional black hole generated by Einstein-Maxwell equations. It has been found that the term derived modifies the repulsive effect of kaluza Klein scalar on world lines. We proved some mathematical theorems which give an insight into the interior of the black holes.