Raychaudhuri equation in spacetimes with torsion

TL;DR

This paper derives the Raychaudhuri equation for timelike and null congruences in spacetimes with generic torsion, revealing how torsion influences the evolution of nearby curves and test particle acceleration.

Contribution

It presents the first derivation of the Raychaudhuri equation in spacetimes with the most general torsion field, extending previous formulations.

Findings

Torsion affects the tangent and orthogonal evolution of congruences.

Presence of torsion contributes to relative acceleration between test particles.

Derived equations apply to both timelike and null curves in torsioned spacetimes.

Abstract

Given a spacetime with nonvanishing torsion, we discuss the equation for the evolution of the separation vector between infinitesimally close curves in a congruence. We show that the presence of a torsion field leads, in general, to tangent and orthogonal effects on the congruence; in particular, the presence of a completely generic torsion field contributes to a relative acceleration between test particles. We derive, for the first time in the literature, the Raychaudhuri equation for a congruence of timelike and null curves in a spacetime with the most generic torsion field.