论文标题
在当地统一的$ n $ -manifolds的共同杀戮向量的协变量分类，并向Kerr-de保姆申请
Covariant classification of conformal Killing vectors of locally conformally flat $n$-manifolds with an application to Kerr-de Sitter
论文作者
论文摘要
我们获得了一种坐标独立的算法，以确定本地合成平面的$ n $ n $γ$ signature $（r，s）$ modulo保形转换$γ$的同伴杀伤向量的类别。这是根据伪 - 正交中的内态性来完成的。对于Riemannian $γ$ case（$ r = 0，s = n $），明确的分类已完整完成。为了应用此结果，我们证明了五个维度，$（λ> 0）$ - 真空，代数特殊的指标，具有非分级光学矩阵，以前由Bernardi de Freitas，Godazgar和Reall研究，与Kerr-De Sitter类似于Kerr-de Sitter类似的Metrics一对一。此类存在于所有维度，其定义属性仅涉及$ \ Mathscr {i} $的属性。两个看似无关的指标类别之间的等效性指出了代数特殊类型的散装时段与NULL Infinity的保形几何形状之间的有趣联系
We obtain a coordinate independent algorithm to determine the class of conformal Killing vectors of a locally conformally flat $n$-metric $γ$ of signature $(r,s)$ modulo conformal transformations of $γ$. This is done in terms of endomorphisms in the pseudo-orthogonal Lie algebra $\mathfrak{o}(r+1,s+1)$ up to conjugation of the its group $O(r+1,s+1)$. The explicit classification is worked out in full for the Riemannian $γ$ case ($r = 0, s = n$). As an application of this result, we prove that the set of five dimensional, $(Λ>0)$-vacuum, algebraically special metrics with non-degenerate optical matrix, previously studied by Bernardi de Freitas, Godazgar and Reall, is in one-to-one correspondence with the metrics in the Kerr-de Sitter-like class. This class exists in all dimensions and its defining properties involve only properties at $\mathscr{I}$. The equivalence between two seemingly unrelated classes of metrics points towards interesting connections between the algebraically special type of the bulk spacetime and the conformal geometry at null infinity
