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General Relativity and Quantum Cosmology, gr-qc
Abstract:
Vacuum gravitational fields admitting a light-like Killing field were
systematically studied starting around 1960. Besides the already known plane
waves, a second class of gravitational wave fields was found. In contrast to
plane waves, their wave surfaces were not flat, but had a negative Gaussian
curvature. Recently, such solutions found attention again as "twisted
gravitational waves". In the paper we review and extend the earlier results. In
suitable coordinates, the metric assumes a simple shape. The waves are then
determined by a single function that satisfies a Laplace equation in
cylindrical coordinates. The "twisted waves" prove to be a special case.
