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

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