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# Kundt spacetime

In mathematical physics, Kundt spacetimes are Lorentzian manifolds admitting a geodesic null congruence with vanishing optical scalars (expansion, twist and shear). A well known member of Kundt class is pp-wave. Ricci-flat Kundt spacetimes in arbitrary dimension are algebraically special. In four dimensions Ricci-flat Kundt metrics of Petrov type III and N are completely known.[1] All VSI spacetimes belong to a subset of the Kundt spacetimes.[2]

References

H. Stephani et. al, Exact solutions of Einstein's field equations, 2nd Edition, Cambridge Univ. Press 2003 (Kundt spacetimes are studied in Chapter 31)

Pravda, V.; Pravdova, A.; Coley, A.; Milson, R. (2002), "All spacetimes with vanishing curvature invariants", Classical Quantum Gravity 19 (23): 6213, arXiv:gr-qc/0209024, doi:10.1088/0264-9381/19/23/318.

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