A ug 2 00 9 A higher-dimensional generalization of the geodesic part of the Goldberg-Sachs theorem

Abstract

In more than four spacetime dimensions, a multiple Weyl-aligned null direction (WAND) need not be geodesic. It is proved that any higher-dimensional Einstein spacetime admitting a non-geodesic multiple WAND also admits a geodesic multiple WAND. All five-dimensional Einstein spacetimes admitting a non-geodesic multiple WAND are determined. 

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