Generalised Kundt waves and their physical interpretation

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.

16 pages including 2 figures. To appear in Classical and Quantum Grav