SPATIALLY AFFINE MOTIONS IN RELATIVITY

Aiming to avoid the limitations that the Herglotz-Noether theorem impo ses on the existence of rigid motions, as defined by Born's rigidity c ondition, we propose an extension of the latter, that we call spatial affinities. We then analyse these motions in Minkowski spacetime and o btain a sort of extension of the Herglotz-Noether theorem: although th e space affinity condition is weaker than Born's rigidity, it does not allow for congruences of worldlines with arbitrary translational and rotational motion on one of these worldlines.