Relativistic particles with torsion in three-dimensional non-vacuum spacetimes

In this paper, we analyze trajectories of spacelike curves that are critical points of a Lagrangian depending on its total torsion. We focus on two important families of spacetimes, generalized Robertson-Walker and standard static spacetimes. For the former, we show that such trajectories are those with a constant curvature. For the latter, we also obtain a characterization in terms of the curvature of the trajectory but in this case measured with an appropriate conformal metric.