Generalised Kundt waves and their physical interpretation

Details Generalised Kundt waves and their physical interpretation Generalised Kundt waves and their physical interpretation

2003-10-16

arxiv.org/abs/gr-qc/0310083v1

Class.Quant.Grav. 21 (2004) 207-222

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

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

Scientific paper

10.1088/0264-9381/21/1/014

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.

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