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

0487350 - MÚ 2019 RIV GB eng J - Journal Article
Ortaggio, Marcello - Pravda, Vojtěch - Pravdová, Alena
On higher dimensional Einstein spacetimes with a non-degenerate double Weyl aligned null direction.
Classical and Quantum Gravity. Roč. 35, č. 7 (2018), č. článku 075004. ISSN 0264-9381. E-ISSN 1361-6382
R&D Projects: GA ČR GB14-37086G
Institutional support: RVO:67985840
Keywords : higher-dimensional gravity * WANDs * Weyl tensor
OECD category: Applied mathematics
Impact factor: 3.487, year: 2018
http://iopscience.iop.org/article/10.1088/1361-6382/aaae25

We prove that higher dimensional Einstein spacetimes which possess a geodesic, non-degenerate double Weyl aligned null direction (WAND) $bl$ must additionally possess a second double WAND (thus being of type D) if either: (a) {the Weyl tensor obeys $C_{abc[d}ell_{e]}ell^c=0$ ($LeftrightarrowPhi_{ij}=0$, i.e.,} the Weyl type is II(abd)), (b) $bl$ is twistfree. Some comments about an extension of the Goldberg-Sachs theorem to six dimensions are also made.
Permanent Link: http://hdl.handle.net/11104/0282004