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arXiv · 1711.04160

On higher dimensional Einstein spacetimes with a non-degenerate double Weyl aligned null direction

Marcello Ortaggio·Vojtěch Pravda·Alena Pravdová
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Abstract

We prove that higher dimensional Einstein spacetimes which possess a geodesic, non-degenerate double Weyl aligned null direction (WAND) $\ell$ must additionally possess a second double WAND (thus being of type D) if either: (a) the Weyl tensor obeys $C_{abc[d}\ell_{e]}\ell^c=0$ ($\Leftrightarrow\Phi_{ij}=0$, i.e., the Weyl type is II(abd)); (b) $\ell$ is twistfree. Some comments about an extension of the Goldberg-Sachs theorem to six dimensions are also made.

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Marcello Ortaggio, Vojtěch Pravda, Alena Pravdová. 2017-11-11. On higher dimensional Einstein spacetimes with a non-degenerate double Weyl aligned null direction. https://doi.org/10.1088/1361-6382%2Faaae25

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