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In general relativity, the monochromatic electromagnetic plane wave spacetime is the analog of the monochromatic plane waves known from Maxwell's theory. The precise definition of the solution is quite complicated but very instructive.
Any exact solution of the Einstein field equation which models an electromagnetic field, must take into account all gravitational effects of the energy and mass of the electromagnetic field. Besides the electromagnetic field, if no matter and non-gravitational fields are present, the Einstein field equation and the Maxwell field equations must be solved simultaneously.
In Maxwell's theory of electromagnetism, one of the most important types of an electromagnetic field are those representing electromagnetic radiation. Of these, the most important examples are the electromagnetic plane waves, in which the radiation has planar wavefronts moving in a specific direction at the speed of light. Of these, the most basic is the monochromatic plane waves, in which only one frequency component is present. This is precisely the phenomenon that this solution model, but in terms of general relativity.
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