Pp-wave spacetime: Difference between revisions

Revision as of 02:53, 24 May 2005 editHillman (talk \| contribs)11,881 edits Altered wording to include nonvacuum pp-waves, changed notation slightly to explain physical meaning of metric functions, added reference.← Previous edit		Revision as of 02:54, 24 May 2005 edit undoHillman (talk \| contribs)11,881 editsNo edit summaryNext edit →
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	The ] are a family of ] of ]. They represent wavelike disturbances in the ] of ] which propagate at the ]. In terms of ], the ] defining a pp-wave spacetime can be written		The ] are a family of ] of ]. They represent wavelike disturbances in the ] of ] which propagate at the ]. In terms of ], the ] defining a pp-wave spacetime can be written

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

Revision as of 02:54, 24 May 2005

The pp-waves are a family of exact solutions of Einstein's field equation. 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

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

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

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

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

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

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