Novel Geometric Gauge Invariance of Autoparallels

TL;DR

This paper introduces a new type of geometric gauge invariance linking autoparallel equations across different Riemann-Cartan spacetimes, revealing that equations of motion can be invariant even when actions are not, with applications to mapping torsion effects.

Contribution

It presents a novel gauge invariance for autoparallel equations in Riemann-Cartan spacetimes and demonstrates its use in transforming actions to simpler geometries.

Findings

Autoparallel equations are invariant under a new gauge transformation.

The gauge transformation maps torsion effects to external fields in Riemann spacetimes.

Transformed actions yield consistent equations of motion with original torsion-inclusive actions.

Abstract

We draw attention to a novel type of geometric gauge invariance relating the autoparallel equations of motion in different Riemann-Cartan spacetimes with each other. The novelty lies in the fact that the equations of motion are invariant even though the actions are not. As an application we use this gauge transformation to map the action of a spinless point particle in a Riemann-Cartan spacetime with a gradient torsion to a purely Riemann spacetime, in which the initial torsion appears as a nongeometric external field. By extremizing the transformed action in the usual way, we obtain the same autoparallel equations of motion as those derived in the initial spacetime with torsion via a recently-discovered variational principle.