On the dispersion of cylindrical impulsive gravitational waves

Abstract

An exact solution, describing the dispersion of a wave packet of gravitational radiation, having initially (at time t=0) an impulsive character, is analysed. The impulsive character of the wave-packet derives from the space-time being flat, except at a radial distance ϖ=ϖ₁ (say) at t=0, and the time-derivative of the Weyl scalars exhibiting δ-function singularities at ϖ=ϖ₁, when t→0. The principal feature of the dispersion is the development of a singularity of the metric function, ν, and of the Weyl scalar, ψ₂, when the wave, after reflection at the centre, collides with the still incoming waves. The evolution of the metric functions and of the Weyl scalars, as the dispersion progresses, is illustrated graphically.