Gravitational waves with distinct wavefronts

TL;DR

This paper explores exact Einstein vacuum solutions describing gravitational waves with unique wavefront geometries, extending known solutions and including electromagnetic wave generalizations, providing explicit forms and new insights into wave propagation.

Contribution

It introduces a family of exact solutions with distinct wavefronts, generalizes Rosen pulse solutions, and incorporates electromagnetic waves with similar wavefront structures.

Findings

Derived explicit solutions for gravitational waves with various wavefront geometries.

Connected these solutions to integral representations generalizing Rosen pulses.

Extended the framework to include electromagnetic waves with similar wavefront characteristics.

Abstract

Exact solutions of Einstein's vacuum equations are considered which describe gravitational waves with distinct wavefronts. A family of such solutions presented recently in which the wavefronts have various geometries and which propagate into a number of physically significant backgrounds is here related to an integral representation which is a generalisation of the Rosen pulse solution for cylindrical waves. A nondiagonal solution is also constructed which is a generalisation of the Rosen pulse, being a cylindrical pulse wave with two states of polarization propagating into a Minkowski background. The solution is given in a complete and explicit form. A further generalisation to include electromagnetic waves with a distinct wavefront of the same type is also discussed.