Torsion and the Gravitational Interaction

TL;DR

This paper demonstrates that the gravitational coupling prescription in theories with curvature and torsion aligns with general relativity, supporting the view that torsion offers an alternative but equivalent description of gravity.

Contribution

It provides a formulation of the gravitational coupling in the presence of torsion using a nonholonomic frame, showing its equivalence to general relativity's prescription.

Findings

Coupling prescription with torsion matches that of general relativity

Torsion does not add new degrees of freedom to gravity

Supports teleparallel view as an alternative formulation

Abstract

By using a nonholonomous-frame formulation of the general covariance principle, seen as an active version of the strong equivalence principle, an analysis of the gravitational coupling prescription in the presence of curvature and torsion is made. The coupling prescription implied by this principle is found to be always equivalent with that of general relativity, a result that reinforces the completeness of this theory, as well as the teleparallel point of view according to which torsion does not represent additional degrees of freedom for gravity, but simply an alternative way of representing the gravitational field.