On the dynamics of relativistic particles with torsion in warped product spacetimes

Abstract

Abstract In this work, we study spacelike trajectories of a relativistic particle model whose Lagrangian is given by the total torsion of its worldline. Once the field equations are established, we investigate the trajectories in two physically relevant families of four-dimensional spacetimes: generalized Robertson–Walker and standard static spacetimes. For the former we obtain both characterization as well as non-existence results for Frenet curves of different orders, which are the curves capable of modeling trajectories. For standard static spacetimes, we obtain a full characterization of the critical curves and present an example in which we can explicitly compute non-trivial trajectories.