Propagation equations for deformable test bodies with microstructure in extended theories of gravity

TL;DR

This paper derives propagation equations for deformable bodies with microstructure in extended gravity theories, showing how matter with microstructure can detect non-Riemannian geometries beyond standard general relativity.

Contribution

It provides new equations of motion in metric-affine gravity that incorporate matter microstructure and clarifies how such matter can probe non-Riemannian spacetime features.

Findings

Test bodies with microstructure can detect non-Riemannian geometry.

Propagation equations generalize previous results in relativity.

Ordinary matter probes only Riemannian geometry.

Abstract

We derive the equations of motion in metric-affine gravity by making use of the conservation laws obtained from Noether's theorem. The results are given in the form of propagation equations for the multipole decomposition of the matter sources in metric-affine gravity, i.e., the canonical energy-momentum current and the hypermomentum current. In particular, the propagation equations allow for a derivation of the equations of motion of test particles in this generalized gravity theory, and allow for direct identification of the couplings between the matter currents and the gauge gravitational field strengths of the theory, namely, the curvature, the torsion, and the nonmetricity. We demonstrate that the possible non-Riemannian spacetime geometry can only be detected with the help of the test bodies that are formed of matter with microstructure. Ordinary gravitating matter, i.e., matter without microscopic internal degrees of freedom, can probe only the Riemannian spacetime geometry. Thereby, we generalize previous results of general relativity and Poincare gauge theory.