Gravitational Waves in General Relativity. III. Exact Plane Waves

Plane gravitational waves are here defined to be non-flat solutions of Einstein's empty space-time field equations which admit as much symmetry as do plane electromagnetic waves, namely, a 5-parameter group of motions. A general plane-wave metric is written down and the properties of plane wave space-times are studied in detail. In particular, their characterization as 'plane' is justified further by the construction of 'sandwich waves' bounded on both sides by (null) hyperplanes in flat space-time. It is shown that the passing of a sandwich wave produces a relative acceleration in free test particles, and inferred from this that such waves transport energy.