Colliding Gravitational Waves

Abstract

NOWHERE should the nonlinear features of general relativity show up more clearly than in the collisional interaction of two gravitational waves. One of the direct consequences of the linearity of Maxwell's equations is that electromagnetic waves pass straight through each other, and this is probably one of the best attested facts of physics. It may readily be demonstrated¹ that such a principle of superposition can never apply to gravitational waves travelling in nonparallel directions, but the precise way in which the waves will diffuse through each other has not hitherto been understood. The problem may have a distinct bearing on observational phenomena, because the gravitational fluxes observed by Weber² appear to be large enough to contribute significantly to the curvature of the universe^3,4, hence large enough to make the linearized approximation invalid (a high frequency approximation has, however, been successfully applied to the cosmological problem by Isaacson⁵). We shall describe here a coordinate system in which the problem of colliding plane waves may be discussed in general relativity; a particular solution expressible in elementary functions and representing at least a portion of such a collisional situation will be given.