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.

16 pages

References in corpus (4)

• Classification of the Weyl Tensor in Higher Dimensions and Applications
• Type D Einstein spacetimes in higher dimensions
• Algebraically special axisymmetric solutions of the higher-dimensional vacuum Einstein equation
• Type II Einstein spacetimes in higher dimensions

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• Weyl double copy in type D spacetime in four and five dimensions
• The Newman-Penrose formalism in quadratic gravity
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• On the uniqueness of the Kerr-(A)dS metric as a type II(D) solution in six dimensions