Gravitational waves in general relativity XI. Cylindrical-spherical waves

Abstract

Further properties of a vacuum metric obtained in an earlier paper, representing a spherical-fronted gravitational wave (which, however, possesses cylindrical symmetry) are derived. This metric is constructed by introducing ‘bending terms’ into Rosen’s metric for cylindrical waves. The way the transition occurs from properties characteristic of cylindrical waves to those of spherical waves is examined. The asymptotic behaviour of the optical parameters and the null tetrad components of the Weyl (Riemann) tensor along an outgoing null geodesic is determined. An interpretation of the axial singularity is given by comparison with an analogous feature in classical electromagnetic wave propagation.