Symmetries of asymptotically flat electrovacuum space–times and radiation

Abstract

Symmetries compatible with asymptotic flatness and admitting gravitational and electromagnetic radiation are studied by using the Bondi–Sachs–van der Burg formalism. It is shown that in axially symmetric electrovacuum space–times in which at least locally a smooth null infinity in the sense of Penrose exists, the only second allowable symmetry is either the translational symmetry or the boost symmetry. Translationally invariant space–times with, in general, a straight “cosmic string” along the axis of symmetry are nonradiative although they can have a nonvanishing news function. The boost-rotation symmetric space–times are radiative. They describe “uniformly accelerated charged particles” or black holes which in general may also be rotating—the axial and an additional Killing vector are not assumed to be hypersurface orthogonal. The general functional forms of both gravitational and electromagnetic news functions, and of the mass aspect and total mass of asymptotically flat boost-rotation symmetric space–times at null infinity are obtained. The expressions for the mass are new even in the case of vacuum boost-rotation symmetric space–times with hypersurface orthogonal Killing vectors. In the Appendices some errors appearing in previous works are corrected.