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This is an old revision of this page, as edited by Hillman (talk | contribs) at 02:53, 24 May 2005 (Altered wording to include nonvacuum pp-waves, changed notation slightly to explain physical meaning of metric functions, added reference.). The present address (URL) is a permanent link to this revision, which may differ significantly from the current revision.

The pp-waves are a family of exact solutions of Einstein's field equations. They represent wavelike disturbances in the curvature of spacetime which propagate at the speed of light. In terms of Brinkmann coordinates, the line element defining a pp-wave spacetime can be written

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

To obtain a null dust solution, we may choose ${\displaystyle H(u,x,y)}$ to be any smooth function. If we require ${\displaystyle H(u,x,y)}$> to be a harmonic function (that is, a solution of the Laplace equation in the variables ${\displaystyle x,y}$), then we obtain a vacuum solution.

An important class of pp-waves are the Baldwin/Jeffery plane waves, which are obtained by choosing

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

Here, if ${\displaystyle c(u)}$ vanishes, we have the plane gravitational waves.

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