A new singularity theorem in relativistic cosmology

TL;DR

This paper presents a new singularity theorem in relativistic cosmology showing that under certain conditions, the space average of scalars in the Raychaudhuri equation vanishes, implying potential singularities.

Contribution

It introduces a novel singularity theorem based on the hypersurface orthogonality of the Ricci tensor's timelike eigenvector and the strong energy condition.

Findings

Space average of scalars in Raychaudhuri equation vanishes under specified conditions

The theorem links hypersurface orthogonality and energy conditions to singularity formation

Provides a new criterion for singularity theorems in cosmology

Abstract

It is shown that if the timelike eigenvector of the Ricci tensor be hypersurface orthogonal so that the space time allows a foliation into space sections then the space average of each of the scalar that appear in the Raychaudhuri equation vanishes provided the strong energy condition holds good. This result is presented in the form of a singularity theorem.