Monochromatic electromagnetic plane wave
The monochromatic electromagnetic plane wave spacetime is an electrovacuum spacetime containing only monochromatic plane waves.
1. History
2. Topology
The monochromatic electromagnetic plane wave spacetime has the topology $\mathbb{R}^4$.
3. Metrics and coordinates
For a plane wave in the $z$ direction, the metric is
$$ds^2 = -2 du dv + C^2 (\frac{q^2}{\omega^2}, 2\frac{q^2}{\omega^2}, \omega u) (dx^2 + dy^2)$$with $C$ the Mathieu cosine function.