标题： $Λ\neq 0$真空代数特殊时空的分类，具有共形平坦的$\mathscr I$从 Weyl 张量展开 显示英文标题

标题： Classification of $Λ\neq 0$-vacuum algebraically special spacetimes with conformally flat $\mathscr I$ from Weyl tensor expansion

摘要： 我们引入了相对于非零向量$u$的类似黎曼和类似威耳逊张量的一般代数分解。 我们推导了类似于高斯、柯达齐和里奇的恒等式，用于威耳逊张量，这些恒等式允许将时空威耳逊张量的分量与正交于$u$的超曲面的内在量相关联。 在限制到$\Lambda$真空时空的情况下（具有$\Lambda \neq 0$和任何维度），并且允许共形紧化，我们通过渐近展开{\it 按照}费弗曼-格雷厄姆来研究威耳逊张量在$\mathscr I$附近的性质，其中前几项被显式计算。 我们使用这些工具来表征具有局部共形平坦的四维代数特殊时空$\mathscr{I}$，表明它们完全匹配所谓的{\it 具有共形平坦的$\scri$类似克尔-德西特类}，从而提供了这类时空的几何表征。 显示英文摘要

摘要： We introduce a general algebraic decomposition of Riemann-like and Weyl-like tensors with respect to a non-null vector $u$. We derive Gauss, Codazzi and Ricci-type identities for the Weyl tensor, that allow to relate the components of the spacetime Weyl tensor with intrinsic quantities of the hypersurfaces orthogonal to $u$. Restricting to the case of $\Lambda$-vacuum spacetimes (with $\Lambda \neq 0$ and any dimension) admiting a conformal compactification, we then study the behaviour of the Weyl tensor near $\mathscr I$ by means of an asymptotic expansion {\it \`a la} Fefferman-Graham, where the first terms are explicitly computed. We use these tools to characterize four dimensional algebraically special spacetimes with locally conformally flat $\mathscr{I}$, showing they match exactly the so-called {\it Kerr-de Sitter-like class with conformally flat $\scri$}, thus providing a geometric characterization of this class of spacetimes.