Pp-wave metrics

The pp-wave metrics describe various types of gravitational waves and are given by:

<math>ds^2=H(u, x, y)du^2+2dudv+dx^2+dy^2<math>

where <math>H<math> is a function of at most 3 variables. An important class of pp-waves are the plane gravitational waves and are obtained by choosing

<math>H(u, x, y)=a(u)x^2+b(u)y^2+c(u)xy<math>