A higher-dimensional generalization of the geodesic part of the Goldberg-Sachs theorem

Understand

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.