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arXiv · gr-qc/0310083

Generalised Kundt waves and their physical interpretation

J. B. Griffiths·P. Docherty·J. Podolsky
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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 ($Λ_c$) 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 $Λ_c$ and type III with $Λ_c=0$. It is shown that there are two, one and three distinct classes of solutions when $Λ_c$ 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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J. B. Griffiths, P. Docherty, J. Podolsky. 2003-10-16. Generalised Kundt waves and their physical interpretation. https://doi.org/10.1088/0264-9381%2F21%2F1%2F014

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