A Class of Collisions of Plane Impulsive Light--Like Signals in General Relativity

TL;DR

This paper systematically analyzes collisions of homogeneous, plane-fronted impulsive light-like signals in general relativity, identifying conditions for non-interaction and providing general solutions that include known cases.

Contribution

It introduces necessary conditions for non-interacting collisions of impulsive light-like signals and derives general solutions under these conditions.

Findings

Two necessary conditions for non-interacting collisions are identified.

The collision solutions focus signals at Weyl curvature singularities.

The family of solutions includes some previously known collision solutions.

Abstract

We present a systematic study of collisions of homogeneous, plane--fronted, impulsive light--like signals which do not interact after head--on collision. For the head--on collision of two such signals, six real parameters are involved, three from each of the incoming signals. We find two necessary conditions to be satisfied by these six parameters for the signals to be non--interacting after collision. We then solve the collision problem in general when these necessary conditions hold. After collision the two signals focus each other at Weyl curvature singularities on each others signal front. Our family of solutions contains some known collision solutions as special cases.