On the collision of impulsive gravitational waves when coupled with fluid motions

Abstract

An exact solution of Einstein’s equations, with a source derived from a perfect fluid in which the energy density, ε , is equal to the pressure, p , is obtained. The solution describes the space–time following the collision of plane impulsive gravitational waves and is the natural generalization of the Nutku─Halil solution of the vacuum equations, in the region of interaction under similar basic conditions. A consistent extension of the solution, prior to the instant of collision, requires that the fluid in the region of interaction is the direct result of a transformation of incident null-dust (i. e. of massless particles describing null trajectories). The ultimate result of the collision is the development of a space─time singularity, the nature of which is strongly dependent on the amplitude and the character of the sound waves that are present. The distribution of ε that follows the collision has many intriguing features. The solution obtained in this paper provides the first example of an induced transformation of a massless into a massive particle.