Singularity theorems and the inclusion of torsion in affine theories of gravity

TL;DR

This paper generalizes singularity theorems in General Relativity to affine theories of gravity with torsion, analyzing how torsion influences the formation of singularities and focal points in Lorentzian manifolds.

Contribution

It extends Raychaudhuri-Komar singularity theorems to include torsion in affine gravity theories, considering both hypersurface orthogonal and accelerated curves.

Findings

Torsion affects the focusing of geodesics and the formation of focal points.

New singularity theorems are proven for Lorentzian manifolds with perfect fluids or scalar fields.

Generalization of classical singularity results to broader affine gravity contexts.

Abstract

We extend the scope of the Raychaudhuri-Komar singularity theorem of General Relativity to affine theories of gravity with and without torsion. We first generalize the existing focusing theorems using time-like and null congruences of curves which are hypersurface orthogonal, showing how the presence of torsion affects the formation of focal points in Lorentzian manifolds. Considering the energy conservation on a given affine gravity theory, we prove new singularity theorems for accelerated curves in the cases of Lorentzian manifolds containing perfect fluids or scalar field matter sources.