Generalised Kundt waves and their physical interpretation

TL;DR

This paper classifies and describes a complete family of Kundt wave space-times with non-zero cosmological constant and aligned radiation, detailing their geometric structures and singularities.

Contribution

It generalizes known vacuum solutions to include non-zero cosmological constants and aligned radiation, providing a comprehensive classification of these Kundt wave space-times.

Findings

Identifies three classes of solutions based on the cosmological constant.

Describes wave surfaces as plane, spherical, or hyperboloidal.

Interprets singularities as envelopes of wave surfaces.

Abstract

We present the complete family of space-times with a non-expanding, shear-free, twist-free, geodesic principal null congruence (Kundt waves) that are of algebraic type III and for which the cosmological constant ($\Lambda_c$) is non-zero. The possible presence of an aligned pure radiation field is also assumed. These space-times generalise the known vacuum solutions of type N with arbitrary $\Lambda_c$ and type III with $\Lambda_c=0$. It is shown that there are two, one and three distinct classes of solutions when $\Lambda_c$ is respectively zero, positive and negative. The wave surfaces are plane, spherical or hyperboloidal in Minkowski, de Sitter or anti-de Sitter backgrounds respectively, and the structure of the family of wave surfaces in the background space-time is described. The weak singularities which occur in these space-times are interpreted in terms of envelopes of the wave surfaces.