On colliding waves in the Einstein—Maxwell theory

Abstract

An exact solution of the Einstein—Maxwell equations is obtained that represents a space-time which describes consistently the collision between two plane impulsive gravitational waves, each supporting an electromagnetic shock-wave. In obtaining the solution, the relationship, which had been established earlier, between the solutions describing stationary black-holes and solutions describing colliding plane-waves, is extended to the Einstein-Maxwell equations (and exploited). The case when the colliding waves are parallelly polarized is analysed in detail to exhibit the singularities and the discontinuities that occur on the null boundaries characteristic of this problem. It is found that the passage of the waves, prior to collision, produces a spray of gravitational and electromagnetic radiation and the collision results in the scattering and the focusing of the waves and the development of a space—time singularity. The solution that is obtained avoids in a natural way certain conceptual difficulties (such as the occurrence of the ‘square root’ of a δ -function and current sheets) that had been anticipated.