Motion of Test Particles in Spacetimes with Torsion and Nonmetricity

TL;DR

This paper derives the equations of motion for test particles with hypermomentum in spacetimes featuring torsion and nonmetricity, providing a method to measure these geometric properties through particle trajectories.

Contribution

It introduces a new approach to observe torsion and nonmetricity by analyzing hypermomentum-charged test particles in non-Riemannian spacetimes.

Findings

Trajectories can reveal torsion and nonmetricity effects

Results align with previous theoretical work

Evaluates the scope of the 'geometrical trinity of gravity'

Abstract

We derive the equations of motion of a test particle with intrinsic hypermomentum in spacetimes with both torsion $S$ and nonmetricity $Q$ (along with curvature $R$). Accordingly, $S$ and $Q$ can be measured by tracing out the trajectory followed by a hypermomentum-charged test particle in such a non-Riemannian background. The test particle is approximated by means of a Dirac $\delta$-function. Thus we find a tangible way to observe and measure the effects of torsion and nonmetricity. Our results are consistent with earlier ones derived by Obukhov and Puetzfeld (2014) by means of a different method. We apply our insight and evaluate how far-reaching the so-called `geometrical trinity of gravity' really is.