Demystifying autoparallels in alternative gravity

TL;DR

This paper clarifies the nature of autoparallel curves in alternative gravity, deriving them as effective constructs and arguing against their use as fundamental equations of motion for test bodies.

Contribution

It explicitly derives autoparallels as post-Riemannian geometric constructs and challenges their role as fundamental equations of motion in alternative gravity theories.

Findings

Autoparallels can be derived as effective geometric constructs.

Autoparallels should not be assumed as fundamental equations of motion.

The paper clarifies the geometric interpretation of autoparallels in alternative gravity.

Abstract

Autoparallel curves along with geodesic curves can arise as trajectories of physical test bodies. We explicitly derive autoparallels as effective post-Riemannian geometric constructs, and at the same time we argue \emph{against} postulating autoparallels as fundamental equations of motion for test bodies in alternative gravity theories.