Plane Fronted Limit of Spherical Electromagnetic and Gravitational Waves

TL;DR

This paper shows how spherical electromagnetic and gravitational waves asymptotically approach plane fronted waves with colliding wave fronts, using Bateman's solutions for electromagnetism and a new form of Robinson-Trautman solutions for gravity.

Contribution

It introduces a novel approach to derive plane fronted waves as limits of spherical waves in both electromagnetic and gravitational contexts.

Findings

Electromagnetic waves are represented using Bateman's solutions.

A new form of Robinson-Trautman solutions describes gravitational waves.

Plane fronted waves are the asymptotic limit of spherical waves.

Abstract

We demonstrate how plane fronted waves with colliding wave fronts are the asymptotic limit of spherical electromagnetic and gravitational waves. In the case of the electromagnetic waves we utilize Bateman's representation of radiative solutions of Maxwell's vacuum field equations. The gravitational case involves a novel form of the radiative Robinson--Trautman solutions of Einstein's vacuum field equations.