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arXiv · 0908.2771

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

Mark Durkee·Harvey S. Reall
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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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Mark Durkee, Harvey S. Reall. 2009-08-19. A higher-dimensional generalization of the geodesic part of the Goldberg-Sachs theorem. https://doi.org/10.1088/0264-9381%2F26%2F24%2F245005

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