Tidal acceleration of autoparallels in metric-affine gravity separates into Newtonian gravity plus linear post-Riemannian corrections from torsion and nonmetricity that can be decomposed into irreducible Lorentz components.
Equations of motion in metric-affine gravity: A covariant unified framework
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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.
fields
gr-qc 2years
2026 2verdicts
UNVERDICTED 2representative citing papers
Metric-affine gravity formulates equivalence principle violations via non-metricity that parallel finite-temperature mass-ratio shifts, and a generalized Fermi-Walker derivative shows no orthonormal tetrad propagates along observer worldlines.
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Tidal Forces in the Presence of Torsion and Nonmetricity
Tidal acceleration of autoparallels in metric-affine gravity separates into Newtonian gravity plus linear post-Riemannian corrections from torsion and nonmetricity that can be decomposed into irreducible Lorentz components.
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Equivalence Principle violation in metric-affine gravity and finite-temperature effects
Metric-affine gravity formulates equivalence principle violations via non-metricity that parallel finite-temperature mass-ratio shifts, and a generalized Fermi-Walker derivative shows no orthonormal tetrad propagates along observer worldlines.