In general relativity, the monochromatic electromagnetic plane we spacetime is the analog of the monochromatic plane wes known from Maxwell's theory. The precise definition of the solution is quite complicated but very instructive.[according to whom?]
Any exact solution of the Einstein field equation which models an electromagnetic field, must take into account all gritational effects of the energy and mass of the electromagnetic field. Besides the electromagnetic field, if no matter and non-gritational fields are present, the Einstein field equation and the Maxwell field equations must be solved simultaneously.
In Maxwell's field theory of electromagnetism, one of the most important types of an electromagnetic field are those representing electromagnetic microwe radiation. Of these, the most important examples are the electromagnetic plane wes, in which the radiation has planar wefronts moving in a specific direction at the speed of light. Of these, the most basic is the monochromatic plane wes, in which only one frequency component is present. This is precisely the phenomenon that this solution model, but in terms of general relativity.
Definition of the solution[edit]The metric tensor of the unique exact solution modeling a linearly polarized electromagnetic plane we with amplitude q and frequency ω can be written, in terms of Rosen coordinates, in the form
d s 2 = − 2 d u d v + C 2 ( q 2 ω 2 , 2 q 2 ω 2 , ω u ) ( d x 2 + d y 2 ) , − ∞