Test particles behavior in the framework of a lagrangian geometric theory with propagating torsion

TL;DR

This paper develops a geometric theory with propagating torsion in vacuum, deriving test particle motion along autoparallels and showing torsion's effects mimic Newtonian gravity, explaining the lack of experimental evidence.

Contribution

It introduces a Lagrangian geometric framework with propagating torsion, deriving wave equations and particle trajectories, and analyzing their phenomenology in the nonrelativistic limit.

Findings

Torsion propagates as waves similar to gravitational waves.

Test particles follow autoparallels in this theory.

Torsion's effects are indistinguishable from Newtonian gravity in the nonrelativistic limit.

Abstract

Working in the lagrangian framework, we develop a geometric theory in vacuum with propagating torsion; the antisymmetric and trace parts of the torsion tensor, considered as derived from local potential fields, are taken and, using the minimal action principle, their field equations are calculated. Actually these will show themselves to be just equations for propagating waves giving torsion a behavior similar to that of metric which, as known, propagates through gravitational waves. Then we establish a principle of minimal substitution to derive test particles equation of motion, obtaining, as result, that they move along autoparallels. We then calculate the analogous of the geodesic deviation for these trajectories and analyze their behavior in the nonrelativistic limit, showing that the torsion trace potential $\phi$ has a phenomenology which is indistinguishable from that of the gravitational newtonian field; in this way we also give a reason for why there have never been evidence for it.