标题： 高维爱因斯坦时空具有非退化双Weyl对齐零方向 显示英文标题

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

摘要： 我们证明了高维爱因斯坦时空如果存在一个测地线、非退化的双Weyl对齐 null 方向（WAND）$\ell$，则必须另外拥有一个双WAND（因此属于类型D），如果满足以下条件之一：(a) Weyl张量满足$C_{abc[d}\ell_{e]}\ell^c=0$($\Leftrightarrow\Phi_{ij}=0$，即Weyl类型为II(abd))；(b)$\ell$是无旋的。还对将Goldberg-Sachs定理扩展到六维的一些评论进行了说明。 显示英文摘要

摘要： 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.