Gravitational plane wave

Gravitational plane waves are described as "non-flat solutions of Albert Einstein’s empty spacetime field equation". They are a special class of a vacuum pp-wave spacetime.

In general relativity, the may be defined in terms of Brinkmann coordinates by

$d{s}^2=[a(u)(x^2-y^2)+2b(u)xy]d{u}^2+2dudv+d{x}^2+d{y}^2$

Here, $a(u),b(u)$ 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.

See also

• vacuum solution (general relativity)