Dynamical torsion and torsion potential

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.