On a Five-Dimensional Version of the Goldberg-Sachs Theorem
The recently developed generalization of the Goldberg-Sachs theorem to five-dimensional Einstein spacetimes is summarized. This generalization involves two steps. First it has been proven that in arbitrary dimension an Eistein spacetime admitting a multiple WAND admits also a multiple geodetic WAND. Second, in five dimensions, the \(3 \times 3\) optical matrix of such geodetic multiple WAND can be cast to one of three canonical forms, each determined by two free parameters.
The authors acknowledge support from research plan RVO: 67985840 and research grant no P203/10/0749.