Can torsion play a role in angular momentum conservation law?

TL;DR

This paper investigates the role of torsion in angular momentum conservation within Einstein-Cartan theory, concluding that torsion does not influence the conservation law under certain tetrad transformations.

Contribution

It demonstrates that, under specific tetrad transformations, torsion does not affect the angular momentum conservation law in Einstein-Cartan theory.

Findings

Torsion tensor cannot influence angular momentum conservation under certain transformations.

The Noether theorem is used to derive covariant angular-momentum conservation.

The conserved current is interpreted as the angular momentum tensor of the gravity-matter system.

Abstract

In Einstein-Cartan theory, by the use of the general Noether theorem, the general covariant angular-momentum conservation law is obtained with the respect to the local Lorentz transformations. The corresponding conservative Noether current is interpreted as the angular momentum tensor of the gravity-matter system including the spin density. It is pointed out that, assuming the tetrad transformation given by eq. (15), torsion tensor can not play a role in the conservation law of angular momentum.