Torsion as Alternative to Curvature in the Description of Gravitation

TL;DR

This paper explores how torsion can serve as an alternative to curvature in describing gravitation, showing that the coupling prescription aligns with general relativity and applying it to Dirac spinors.

Contribution

It demonstrates the equivalence of torsion-based and curvature-based gravitational coupling prescriptions within the framework of general covariance.

Findings

Coupling prescriptions with torsion are equivalent to those with curvature.

The approach is consistent with the principle of equivalence.

Application to Dirac spinors confirms the theoretical framework.

Abstract

The general covariance principle, seen as an active version of the principle of equivalence, is used to study the gravitational coupling prescription in the presence of curvature and torsion. It is concluded that the coupling prescription determined by this principle is always equivalent with the corresponding prescription of general relativity. An application to the case of a Dirac spinor is made.