Tidal Forces in the Presence of Torsion and Nonmetricity

This work investigates how torsion and nonmetricity modify tidal accelerations in metric-affine gravity.

We derive a projected deviation equation that generalizes the standard geodesic deviation equation to metric-affine geometry, and apply it to the relative acceleration of neighboring autoparallels in the weak-field, nonrelativistic limit.

In this regime, the tidal acceleration separates into the usual Newtonian contribution and linear post-Riemannian corrections sourced by torsion and non-metricity.

By decomposing torsion and nonmetricity into their irreducible Lorentz components, we identify the corresponding signatures in the tidal tensor and discuss to what extent these contributions can be distinguished.

We then show how future direct tidal measurements could be translated into benchmark bounds on post-Riemannian tidal contributions, assuming probe dynamics sensitive to the affine connection.

Our results suggest that the tidal acceleration may provide a systematic route toward probing post-Riemannian spacetime features in the future.