Probing non-Riemannian spacetime geometry

TL;DR

This paper derives matter equations of motion in non-Riemannian spacetimes, showing only microstructured test bodies couple to torsion, and concludes that satellite experiments like Gravity Probe B cannot detect spacetime torsion.

Contribution

It provides a derivation of matter motion equations in non-Riemannian geometry and clarifies the detectability of torsion with satellite experiments.

Findings

Test bodies with microstructure couple to non-Riemannian geometry.

Gravity Probe B cannot detect spacetime torsion.

Spacetime torsion remains undetectable with certain satellite experiments.

Abstract

The equations of motion for matter in non-Riemannian spacetimes are derived via a multipole method. It is found that only test bodies with microstructure couple to the non-Riemannian spacetime geometry. Consequently it is impossible to detect spacetime torsion with the satellite experiment Gravity Probe B, contrary to some recent claims in the literature.