Diverging type-D metrics

Abstract

This paper contains an investigation of algebraically special spaces with two commuting Killing vectors. It is shown that the field equations for these spaces can be reduced to two ordinary differential equations, one of which is quasi-linear in one of the variables. The metric is type D iff it possesses a two dimensional, abelian, orthogonally transitive symmetry group. Finally, the type D metrics of Kinnersley are expressed in various coordinates, including those of Plebanski and Demianski