Abstract

AbstractWe collect results that characterize trajectories of relativistic particle models defined by functionals depending linearly either on the curvature or the torsion. Such curves are assumed to live in spacelike slices of three-dimensional spacetimes belonging to two families: Generalized Robertson-Walker spacetimes (GRWs) and standard static spacetimes. Whereas the curvature functional on three-dimensional GRWs and the torsion functional on three-dimensional GRWs and standard static spacetimes were discussed in previous studies, the calculations concerning the trajectories of the curvature functional on three-dimensional standard static spacetimes constitute an original piece of research.

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