Equations of motion in metric-affine gravity: A covariant unified framework

TL;DR

This paper develops a covariant framework for deriving the equations of motion of extended bodies in metric-affine gravity, revealing conditions under which post-Riemannian geometry can be detected via test bodies.

Contribution

It introduces a unified covariant approach using Synge's world function to derive motion equations in metric-affine gravity, extending previous results.

Findings

Detection of post-Riemannian geometry requires nonminimal coupling to matter.

Unified equations of motion for extended bodies in metric-affine gravity.

Confirmation that microstructured bodies are needed to probe certain geometries.

Abstract

We derive the equations of motion of extended deformable bodies in metric-affine gravity. The conservation laws which follow from the invariance of the action under the general coordinate transformations are used as a starting point for the discussion of the dynamics of extended deformable test bodies. By means of a covariant approach, based on Synge's world function, we obtain the master equation of motion for an arbitrary system of coupled conserved currents. This unified framework is then applied to metric-affine gravity. We confirm and extend earlier findings; in particular, we once again demonstrate that it is only possible to detect the post-Riemannian spacetime geometry by ordinary (non-microstructured) test bodies if gravity is nonminimally coupled to matter.