Plane Gravitational Waves in General Relativity

Abstract

POLARIZED plane gravitational waves were first discovered by N. Rosen¹, who, however, came to the conclusion that such waves could not exist because the metric would have to contain certain physical singularities. More recent work by Taub² and McVittie³ showed that there were no unpolarized plane waves, and this result has tended to confirm the view that true plane gravitational waves do not exist in empty space in general relativity. Partly owing to this, Scheidegger⁴ and I⁵ have both expressed the opinion that there might be no energy-carrying gravitational waves at all in the theory. It is therefore of interest to point out, as was first shown by Robinson⁶ and has now been independently proved by me, that Rosen's argument is invalid and that true gravitational waves do in fact exist. Moreover, it is shown here that these waves carry energy, although it has not yet been possible to relate the intensity of the wave to the amount of energy carried.