Symmetries of asymptotically flat axisymmetric space–times with null dust

Abstract

Symmetries of space–times with null dust field as a source compatible with asymptotic flatness are studied by using the Bondi–Sachs–van der Burg formalism. It is shown that in an axially symmetric space–time with null dust field in which at least locally a smooth null infinity in the sense of Penrose exists, the only allowable additional Killing vector forming with the axial one a two-dimensional Lie algebra (the axial and the additional Killing vector are not assumed to be hypersurface orthogonal) is a supertranslational Killing vector and the gravitational field is then nonradiative (the Weyl tensor has a nonradiative character).