Null congruence spacetimes constructed from 3-dimensional Robertson–Walker spaces

Null congruence spacetimes are constructed from three-dimensional time-orientable Lorentzian manifolds by taking a particular ellipse in the lightcone above every point. Starting from a three-dimensional Robertson–Walker space, new null congruence spacetimes are obtained and several of their curvature properties are deduced. In particular, it is shown that the static Einstein universe is locally isometric to a certain null congruence spacetime. Furthermore, a method is given to construct trapped surfaces which admit an isometric spacelike circle action in null congruence spacetimes.