Plane fronted electromagnetic waves and an asymptotic limit of Li\'enard--Wiechert fields

TL;DR

This paper investigates the asymptotic behavior of Lie9nard--Wiechert electromagnetic fields, revealing how colliding plane fronted waves encode source motion information and providing a detailed Maxwell field analysis.

Contribution

It constructs an asymptotic limit of Lie9nard--Wiechert fields in Minkowski space, offering a detailed algebraically general Maxwell field with colliding plane waves.

Findings

Derived an algebraically general Maxwell field with colliding plane waves.

Provided a detailed analysis of Lie9nard--Wiechert fields' asymptotic limit.

Gave a new perspective on a Maxwell field discovered by Bateman.

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 Li\'enard--Wiechert electromagnetic fields in the context of Minkowskian space--time. 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 space--time and an interesting byproduct is a novel perspective on a Maxwell field originally discovered by Bateman.