Behavior of Einstein-Rosen waves at null infinity

The asymptotic behavior of Einstein-Rosen waves at null infinity in four dimensions is investigated in all directions by exploiting the relation between the four-dimensional space-time and the three-dimensional symmetry reduction thereof. Somewhat surprisingly, the behavior in a generic direction is better than that in directions orthogonal to the symmetry axis. The geometric origin of this difference can be understood most clearly from the three-dimensional perspective.