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.