Vacuum Kerr-Schild metrics generated by nontwisting congruences



The Kerr-Schild pencil of metrics gab = gab + Vlalb, with gab and gab satisfying the vacuum Einstein equations, is investigated in the case when the null vector l has vanishing twist. This class of Kerr-Schild metrics contains two solutions: the Kasner metric and a metric which can be obtained from the Kasner metric by a complex coordinate transformation. Both are limiting cases of the Kóta-Perjés metrics. The base space-time is a pp-wave.