Born's group and Generalized isometries

Abstract

We define the Born group as the group of transformations that leave invariant the line element of Minkowski's spacetime written in terms of Fermi coordinates of a Born congruence. This group depends on three arbitrary functions of a single argument. We construct implicitly the finite transformations of this group and explicitly the corresponding infinitesimal ones. Our analysis of this group brings out the new concept of Generalized group of isometries. The limitting cases of such groups being, at one end, the Groups of isometries of a spacetime metric and, at the other end, the Group of diffeomorphisms of any spacetime manifold. We mention two examples of potentially interesting generalizations of the Born congruences.