The Bell-Szekeres Solution and Related Solutions of the Einstein-Maxwell Equations

TL;DR

This paper introduces a new method for solving Einstein-Maxwell equations related to light-like signal collisions, extending the classic Bell-Szekeres solution to include shells and gravitational waves, revealing new solution families.

Contribution

A novel technique for solving Einstein-Maxwell equations is developed, extending the Bell-Szekeres solution to include additional physical scenarios such as shells and gravitational waves.

Findings

Extended Bell-Szekeres solutions including light-like shells.

Derived a family of solutions with similar geometrical properties.

Provided a new approach to collision problems in Einstein-Maxwell theory.

Abstract

A novel technique for solving some head-on collisions of plane homogeneous light-like signals in Einstein-Maxwell theory is described. The technique is a by-product of a re-examination of the fundamental Bell-Szekeres solution in this field of study. Extensions of the Bell-Szekeres collision problem to include light-like shells and gravitational waves are described and a family of solutions having geometrical and topological properties in common with the Bell-Szekeres solution is derived.