Monochromatic Electromagnetic Plane Wave
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 a bit 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 of the electromagnetic field itself. If there is no matter and no non-gravitational fields present other than the electromagnetic field, this means that we must simultaneously solve the Einstein field equation and the (curved spacetime, source-free) Maxwell field equations.
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 are the monochromatic plane waves, in which only one frequency component is present. This is precisely the phenomenon which our solution will model in terms of general relativity.
Read more about Monochromatic Electromagnetic Plane Wave: Definition of The Solution, Local Isometries, A Family of Inertial Observers, The Electromagnetic Field, Relative Motion of The Observers, The Riemann Curvature Tensor, Optical Effects, The Brinkmann Chart, Caustics, Summary
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