Gravitational plane wave
Encyclopedia
In general relativity
, a gravitational plane wave is a special class of a vacuum pp-wave spacetime
, and may be defined in terms of Brinkmann coordinates
by
Here,
can be any smooth function
s; 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.
General relativity
General relativity or the general theory of relativity is the geometric theory of gravitation published by Albert Einstein in 1916. It is the current description of gravitation in modern physics...
, a gravitational plane wave is a special class of a vacuum pp-wave spacetime
Pp-wave spacetime
In general relativity, the pp-wave spacetimes, or pp-waves for short, are an important family of exact solutions of Einstein's field equation. These solutions model radiation moving at the speed of light...
, and may be defined in terms of Brinkmann coordinates
Brinkmann coordinates
Brinkmann coordinates are a particular coordinate system for a spacetime belonging to the family of pp-wave metrics. In terms of these coordinates, the metric tensor can be written asds^2 \, = H du^2 + 2 du dv + dx^2 + dy^2...
by
Here,
can be any smooth functionSmooth function
In mathematical analysis, a differentiability class is a classification of functions according to the properties of their derivatives. Higher order differentiability classes correspond to the existence of more derivatives. Functions that have derivatives of all orders are called smooth.Most of...
s; they control the waveform
Waveform
Waveform means the shape and form of a signal such as a wave moving in a physical medium or an abstract representation.In many cases the medium in which the wave is being propagated does not permit a direct visual image of the form. In these cases, the term 'waveform' refers to the shape of a graph...
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.