Autoparallels From a New Action Principle

TL;DR

This paper introduces a simplified action principle for spinless particles in curved spacetimes with torsion, showing that metric-only actions can yield autoparallel equations of motion through noncommutative variations.

Contribution

It presents a new, more powerful action principle that derives autoparallel motion from a metric-only action, highlighting the role of noncommutative variations in torsionful geometries.

Findings

Metric-only action produces torsion-induced autoparallels

Noncommutativity of variations explains torsion force

Simplifies derivation of particle motion in torsionful spacetimes

Abstract

We present a simpler and more powerful version of the recently-discovered action principle for the motion of a spinless point particle in spacetimes with curvature and torsion. The surprising feature of the new principle is that an action involving only the metric can produce an equation of motion with a torsion force, thus changing geodesics to autoparallels. This additional torsion force arises from a noncommutativity of variations with parameter derivatives of the paths due to the closure failure of parallelograms in the presence of torsion