Quantum mechanics

Curvature

Spacetime

Pure mathematics

Mathematical physics

Surgery

Geodesic

Solving the geodesic equations

Classical mechanics

Torsion (gastropod)

Physics

Geodesics in general relativity

Mathematics

Mathematical analysis

Geometry

Congruence relation

Medicine

Physical review. D/Physical review. D.

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.

Raychaudhuri and optical equations for null geodesic congruences with torsion