Torsion and Gravitation: A new view

TL;DR

This paper explores the teleparallel equivalent of general relativity, proposing a new gravitational coupling prescription that maintains the equivalence between curvature and torsion, and applies it to particle motion.

Contribution

It introduces a novel coupling prescription in the presence of torsion and curvature that preserves their equivalence and aligns with standard general relativity.

Findings

Torsion acts as a true gravitational force unlike curvature.

The new coupling prescription is equivalent to the usual one in general relativity.

Application to particle equations of motion confirms the consistency of the approach.

Abstract

According to the teleparallel equivalent of general relativity, curvature and torsion are two equivalent ways of describing the same gravitational field. Despite equivalent, however, they act differently: whereas curvature yields a geometric description, in which the concept of gravitational force is absent, torsion acts as a true gravitational force, quite similar to the Lorentz force of electrodynamics. As a consequence, the right-hand side of a spinless-particle equation of motion (which would represent a gravitational force) is always zero in the geometric description, but not in the teleparallel case. This means essentially that the gravitational coupling prescription can be minimal only in the geometric case. Relying on this property, a new gravitational coupling prescription in the presence of curvature and torsion is proposed. It is constructed in such a way to preserve the equivalence between curvature and torsion, and its basic property is to be equivalent with the usual coupling prescription of general relativity. According to this view, no new physics is connected with torsion, which appears as a mere alternative to curvature in the description of gravitation. An application of this formulation to the equations of motion of both a spinless and a spinning particle is made