Fermionic current in general relativity

TL;DR

This paper explores the role of fermionic currents and torsion in general relativity and Einstein-Cartan theory, analyzing spinor interactions, torsion contributions, and their relation to gravitomagnetism within linearized gravity.

Contribution

It investigates fermionic currents and torsion effects in general relativity using Einstein-Cartan theory, highlighting differences in interaction terms and their physical implications.

Findings

Fermionic rotational current is linked to torsion via Cartan's equations.

Torsion contributions persist even with symmetric affine connections.

Spin connection terms cancel out in linearized gravity, indicating different interaction mechanisms.

Abstract

In general relativity the affine connection is required to be symmetric so torsion is zero while according to the Einsten- Cartan's theory torsion is connected to the spin tensor as expressed by the Cartan's equations. We consider the theory of spinors in general relativity in the light of the results of Einstein Cartan's theory.In general relativity the affine connection is required to be symmetric so torsion is zero while according to the Einsten- Cartan's theory torsion is connected to the spin tensor as expressed by the Cartan's equations. We consider the theory of spinors in general relativity in the light of the results of Einstein Cartan's theory. This work begins with the study of the spin connection coefficients, the calculation of the canonical momenta detects a spinor rotational current; fermionic rotational current is associated with torsion as explained by Cartan's equations, we find this torsion contribution even if the affine connection is symmetric. In the final considerations, we analyze the interaction terms (as written in the full action for Dirac spinors) and we compare them with the results of linearized gravity. We deduce that Gravitomagnetism is well described in the linearized theory while the term of spin connection giving rise to fermionic current is canceled out, so we mean these terms are describing different interactions.