Dynamical torsion and torsion potential

TL;DR

This paper introduces a dynamic torsion potential via a generalized tetrad, deriving coupled Einstein and torsion field equations, and explores its properties and scalar field example within Einstein-Cartan theory.

Contribution

It presents a novel formulation where torsion is described by a potential, making torsion dynamic and coupled to matter fields in Einstein-Cartan theory.

Findings

Derived Einstein and torsion field equations with torsion potential as a matter field

Analyzed properties of local linear transformations of the torsion potential

Provided an example of torsion potential described by a scalar field

Abstract

We introduce a generalized tetrad which plays the role of a potential for torsion and makes torsion dynamic. Starting from the Einstein-Cartan action with torsion, we get two field equations, the Einstein equation and the torsion field equation by using the metric tensor and the torsion potential as independent variables; in the former equation the torsion potential plays the role of a matter field. We also discuss properties of local linear transformations of the torsion potential and give a simple example in which the torsion potential is described by a scalar field.