Gravitational Lorentz Force and the Description of the Gravitational Interaction

TL;DR

This paper derives a gravitational analog of the Lorentz force within a gauge theory framework, showing that scalar matter interacts equivalently with teleparallel and Riemannian geometries, leading to the same particle trajectories.

Contribution

It introduces a unified force equation for scalar particles in gravitational fields, demonstrating the equivalence of teleparallel and Riemannian descriptions of gravity.

Findings

Scalar matter interacts with both teleparallel and Riemannian geometries.

The force equations in both frameworks produce identical particle trajectories.

Teleparallel torsion acts as a force analogous to the Lorentz force.

Abstract

In the context of a gauge theory for the translation group, we have obtained, for a spinless particle, a gravitational analog of the Lorentz force. Then, we have shown that this force equation can be rewritten in terms of magnitudes related to either the teleparallel or the riemannian structures induced in spacetime by the presence of the gravitational field. In the first case, it gives a force equation, with torsion playing the role of force. In the second, it gives the usual geodesic equation of General Relativity. The main conclusion is that scalar matter is able to feel anyone of the above spacetime geometries, the teleparallel and the metric ones. Furthermore, both descriptions are found to be completely equivalent in the sense that they give the same physical trajectory for a spinless particle in a gravitational field.