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The ] may be defined in terms of ] by the ]: The ] may be defined in terms of ] by


<math>ds^2=du^2+2dudv+dx^2+dy^2</math> <math>ds^2=du^2+2dudv+dx^2+dy^2</math>

Revision as of 05:01, 24 May 2005

The plane gravitational waves may be defined in terms of Brinkmann coordinates by

d s 2 = [ a ( u ) ( x 2 − y 2 ) + 2 b ( u ) x y ] d u 2 + 2 d u d v + d x 2 + d y 2 {\displaystyle ds^{2}=du^{2}+2dudv+dx^{2}+dy^{2}}

Here, a ( u ) , b ( u ) {\displaystyle a(u),b(u)} can be any smooth functions; they control the waveform of the two possible polarization modes of gravitational radiation. In this context, these two modes are usually called the plus mode and cross mode, respectively.