Axisymmetric electrovacuum spacetimes with a translational Killing vector at null infinity

TL;DR

This paper investigates the asymptotic structure of axisymmetric electrovacuum spacetimes with a translational Killing vector at null infinity, revealing conditions for stationarity, the presence of a non-radiative news function, and explicit examples involving strings and waves.

Contribution

It provides a detailed analysis of null infinity in such spacetimes, establishing when they are stationary or radiative, and includes explicit examples with strings and cylindrical waves.

Findings

Non-vanishing news function exists without radiation due to strings.

Null infinity's smoothness implies spacetime stationarity if not flat.

Boost symmetry leads to radiative, accelerated spacetimes.

Abstract

By using the Bondi-Sachs-van der Burg formalism we analyze the asymptotic properties at null infinity of axisymmetric electrovacuum spacetimes with a translational Killing vector and, in general, an infinite ``cosmic string'' (represented by a conical singularity) along the axis. Such spacetimes admit only a local null infinity. There is a non-vanishing news function due to the existence of the string even though there is no radiation. We prove that if null infinity has a smooth compact cross section and the spacetime is not flat in a neighbourhood of null infinity, then the translational Killing vector must be timelike and the spacetime is stationary. The other case in which an additional symmetry of axisymmetric spacetimes admits compact cross sections of null infinity is the boost symmetry, which leads to radiative spacetimes representing ``uniformly accelerated objects''. These cases were analyzed in detail in our previous works. If the translational Killing vector is spacelike or null, corresponding to cylindrical or plane waves, some complete generators of null infinity are ``singular'' but null infinity itself can be smooth apart from these generators. As two explicit examples of local null infinity, Schwarzschild spacetime with a string and a class of cylindrical waves with a string are discussed in detail in the Appendix.