Spatially affine motions in relativity

Abstract

Aiming to avoid the limitations that the Herglotz - Noether theorem imposes on the existence of rigid motions, as defined by Born's rigidity condition, we propose an extension of the latter, that we call spatial affinities. We then analyse these motions in Minkowski spacetime and obtain a sort of extension of the Herglotz - Noether theorem: although the 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.