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

${\displaystyle ds^{2}=H(u,x,y)du^{2}+2dudv+dx^{2}+dy^{2}}$

where ${\displaystyle H}$ is a function of at most 3 variables. An important class of pp-waves are the plane gravitational waves and are obtained by choosing

${\displaystyle H(u,x,y)=a(u)x^{2}+b(u)y^{2}+c(u)xy}$

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