Autoparallel deviation with torsion and non-metricity

Abstract

We study the effects of torsion and non-metricity on the deviation between nearby autoparallel curves in spacetime. We show that for any spacetime with torsion and non-metricity, autoparallel deviation is equal to the Riemann curvature tensor and a collection of torsion and non-metricity terms. We also show that the neighboring autoparallel curves for any spacetime, in general, will experience relative time delays, in contrast to the geodesic deviation in general relativity.