Misplaced Pages

Pp-wave spacetime: Difference between revisions

Article snapshot taken from Wikipedia with creative commons attribution-sharealike license. Give it a read and then ask your questions in the chat. We can research this topic together.
Browse history interactively← Previous editNext edit →Content deleted Content addedVisualWikitext
Revision as of 23:01, 8 April 2005 editBRW (talk | contribs)Extended confirmed users, Pending changes reviewers4,280 editsm stub← Previous edit Revision as of 02:53, 24 May 2005 edit undoHillman (talk | contribs)11,881 edits Altered wording to include nonvacuum pp-waves, changed notation slightly to explain physical meaning of metric functions, added reference.Next edit →
Line 1: Line 1:
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 ] describe various types of ] and are given by:


<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>


To obtain a ], we may choose <math>H(u,x,y)</math> to be any ]. If we require <math>H(u,x,y)</math>> to be a ] (that is, a solution of the ] in the variables <math>x,y</math>), then we obtain a ].
⚫ where <math>H</math> is a function of at most 3 variables. An important class of pp-waves are the ] and are obtained by choosing


⚫ An important class of pp-waves are the ], which are obtained by choosing
⚫ <math>H(u, x, y)=a(u)x^2+b(u)y^2+c(u)xy</math>

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

Here, if <math>c(u)</math> vanishes, we have the ].


{{physics-stub}} {{physics-stub}}

Revision as of 02:53, 24 May 2005

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

d s 2 = H ( u , x , y ) d u 2 + 2 d u d v + d x 2 + d y 2 {\displaystyle 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 ) {\displaystyle H(u,x,y)} to be any smooth function. If we require H ( u , x , y ) {\displaystyle H(u,x,y)} > to be a harmonic function (that is, a solution of the Laplace equation in the variables x , y {\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

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

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

Stub icon

This physics-related article is a stub. You can help Misplaced Pages by expanding it.

Categories: