Axisymmetric electrovacuum spacetimes with a translational Killing vector at null infinity

By using the Bondi-Sachs-van der Bug formalism we analyse the asymptotic pr operties at null infinity of axisymmetric electrovacuum spacetimes with a t ranslational Killing vector and, in general, an infinite 'cosmic string' (r epresented by a conical singularity) along the axis. Such spacetimes admit only a local null infinity. There is a non-vanishing news function due to t he existence of the string even though there is no radiation. We prove that if null infinity has a smooth compact cross section and the B ondi mass is nonvanishing, then the translational Killing vector must be ti melike and the spacetime is stationary. The other case in which an addition al symmetry of axisymmetric spacetimes admits compact cross sections of nul l infinity is the boost symmetry, which leads to radiative spacetimes repre senting 'uniformly accelerated objects'. These cases were analysed in detai l in our previous works. If the translational Killing vector is spacelike o r null, corresponding to cylindrical or plane waves, some complete generato rs of null infinity are 'singular' but null infinity itself can be smooth a part from these generators. As two explicit examples of local null infinity, Schwarzschild spacetime wi th a string and a class of cylindrical waves with a string are discussed in detail in the appendix.