Nonlinear gravitational waves, their polarization, and realistic sources

We describe exact solutions of the Einstein field equations invariant under a non-Abelian two-dimensional Lie algebra of Killing fields. A subclass of these gravitational fields have a wavelike character. We show that they have spin $1$. We also discuss some indirect observational effects. In particular, we show that vector cosmological perturbations can no longer be negligible in the presence of topological defects, which can be verified by examining the anisotropies of the cosmic microwave background.