Effect of Spin-Torsion Interaction on Raychaudhuri Equation

TL;DR

This paper generalizes the Raychaudhuri equation within a more comprehensive absolute parallelism geometry, incorporating spin-torsion interactions, which could influence gravitational singularity theorems.

Contribution

It introduces a generalized Raychaudhuri equation accounting for spin-torsion interactions in a broader geometric framework, extending the classical formulation.

Findings

Extra torsion-dependent terms in the equation

Potential impact on singularity theorems

Reduction to original equation under specific conditions

Abstract

Raychaudhuri equation is generalized in the parameterized absolute parallelism geometry. This version of absolute parallelism is more general than the conventional one. The generalization takes into account the suggested interaction between the quantum spin of the moving elementary particle and the torsion of the background gravitational field. The generalized Raychaudhuri equation obtained contains some extra terms, depending on the torsion of space-time, that would have some effects on the singularity theorems of general relativity. Under a certain condition, this equation could be reduced to the original Raychaudhuri equation without any need for a vanishing torsion.