Raychaudhuri and optical equations for null geodesic congruences with torsion

TL;DR

This paper investigates null geodesic congruences in spacetimes with torsion, revealing how torsion's highest spin component influences geodesic acceleration and optical properties, extending classical optical equations to non-Riemannian geometries.

Contribution

It extends the optical equations for null geodesic congruences to include effects of spacetime torsion, highlighting the role of the highest spin torsion component.

Findings

Highest spin torsion causes proper acceleration of geodesics.

Torsion obstructs abreastness of geodesics.

Optical equations depend on non-Riemannian curvature components.

Abstract

We study null geodesic congruences (NGCs) in the presence of spacetime torsion, recovering and extending results in the literature. Only the highest spin irreducible component of torsion gives a proper acceleration with respect to metric NGCs, but at the same time obstructs abreastness of the geodesics. This means that it is necessary to follow the evolution of the drift term in the optical equations, and not just shear, twist and expansion. We show how the optical equations depend on the non-Riemannian components of the curvature, and how they reduce to the metric ones when the highest spin component of torsion vanishes.