Riemannian and Teleparallel Descriptions of the Scalar Field Gravitational Interaction

TL;DR

This paper demonstrates that scalar fields can interact with both metric and teleparallel geometries, producing torsion and establishing their equivalence in describing gravitational interactions.

Contribution

It reveals that scalar matter can detect and produce torsion, challenging the belief that only spin matter interacts with teleparallel geometry, and shows the equivalence of the two descriptions.

Findings

Scalar fields can produce torsion in teleparallel geometry.

Scalar matter interacts with both metric and torsion-based geometries.

The metric and teleparallel descriptions of gravity are equivalent for scalar fields.

Abstract

A comparative study between the metric and the teleparallel descriptions of gravitation is made for the case of a scalar field. In contrast to the current belief that only spin matter could detect the teleparallel geometry, scalar matter being able to feel the metric geometry only, we show that a scalar field is able not only to feel anyone of these geometries, but also to produce torsion. Furthermore, both descriptions are found to be completely equivalent, which means that in fact, besides coupling to curvature, a scalar field couples also to torsion.