A Note on Asymptotically Flat Spaces

Abstract

It is shown that there is a simple alternative to the Bondi type of coordinate condition in asymptotically flat spaces, which leads to a different asymptotic coordinate group whose structure is simpler than that of the BMS group. As a concomitant to this work, there was discovered a scalar function on null infinity. From an analysis of this function one can obtain, starting from the asymptotic shear of one family of hypersurface orthogonal rays, (1) all null asymptotically shear-free congruences, (2) the asymptotic shear of all hypersurface orthogonal rays.