Self-scattering of a Smooth Toroidal Gravitational Pulse Wave

Abstract

IMPORTANT information in astronomy may be gained in the not-too-distant future by the observation of gravitational waves. But the nonlinearity of the gravitational field equations in general relativity makes it difficult to estimate effects which might arise through collisions between waves, even when the nature of the impinging waves is known. In general, direct superposition of solutions for individual waves will lead to violation of the vacuum equations. One thus has to determine, in a particular situation, whether there exists a valid vacuum solution, non-singular in the wave region, which represents the gravitational field before, during and after the collision, or whether instead the eventual formation of physical singularities is predicted. For example, Penrose¹ has shown that in the collision of (exact) weak “sandwich” plane waves², each will warp the other until singularities occur in the wave-front.