Teleparallel gauge theory of gravity

TL;DR

This paper explores a conformally invariant tetrad gravity theory where the torsion tensor's trace acts like an electromagnetic potential, successfully reproducing Newtonian gravity in the linearized vacuum limit.

Contribution

It introduces a novel tetrad gravity model invariant under conformal transformations, with a Maxwell-like action and solutions for static, spherically symmetric spacetimes.

Findings

All static, spherically symmetric vacuum solutions are found.

The Newtonian limit is recovered in the linearized gauge.

The theory's action resembles electromagnetism, with torsion trace as gauge potential.

Abstract

In this work a tetrad theory of gravity, invariant under conformal transformations, is investigated. The action of the theory is similar to the action of Maxwell's electromagnetism. The role of the electromagnetic gauge potential is played by the trace of the torsion tensor of the Weitzenb\"ock spacetime. It is shown that all static, spherically symmetric space-times, are solutions of the vacuum field equations. However, by fixing the gauge in the linearized form of the vacuum field equations, the usual Newtonian limit for the gravitational field is obtained.