Plane-fronted electromagnetic waves and an asymptotic limit of Liénard–Wiechert fields

Abstract

Colliding or noncolliding plane-fronted electromagnetic or gravitational waves are the asymptotic limit of Robinson–Trautman spherical electromagnetic or gravitational waves. Noncolliding plane-fronted waves contain no information about their sources whereas colliding waves contain information about possibly the motion of their sources. As a first step to investigate the latter phenomenon, we construct an asymptotic limit of Liénard–Wiechert electromagnetic fields in the context of Minkowskian spacetime. This has the advantage that the source is well known and the calculations can be carried out in full detail. The final result is an algebraically general Maxwell field which consists of colliding plane-fronted waves in a subregion of Minkowskian spacetime and an interesting byproduct is a novel perspective on a Maxwell field originally discovered by Bateman.