具有$(D-3)$交换转动对称的$D$ -维中的所有真空近视界几何
All Vacuum Near-Horizon Geometries in $D$-dimensions with $(D-3)$ Commuting Rotational Symmetries
摘要：
我们明确地构建所有的固定的，非静态的，极端的近地平线的$D$维几何满足真空爱因斯坦方程，并有$D-3$交换旋转对称性。我们的工作推广了Kunduri和Lucietti的[arXiv：0806.2051]，在$D=4,5$中已经给出了这样的分类。但我们的方法与他们的不同，依赖于爱因斯坦方程的矩阵公式。与他们的方法不同，这个矩阵公式适用于任何维度。我们发现的度量分为三个家族，具有水平拓扑$S^2 \times T^{D-4}$或$S^3 \times T^{D-5}$或其衍生物。我们的度量依赖于两个离散参数指定的拓扑类型，以及$(D-2)(D-3)/2$连续参数。并非所有我们在$D \ge 6$中的度量都出现在已知黑洞解的近视界极限。
英文摘要：
We explicitly construct all stationary, non-static, extremal near horizon geometries in $D$ dimensions that satisfy the vacuum Einstein equations, and that have $D-3$ commuting rotational symmetries. Our work generalizes [arXiv:0806.2051] by Kunduri and Lucietti, where such a classification had been given in $D=4,5$. But our method is different from theirs and relies on a matrix formulation of the Einstein equations. Unlike their method, this matrix formulation works for any dimension. The metrics that we find come in three families, with horizon topology $S^2 \times T^{D-4}$, or $S^3 \times T^{D-5}$, or quotients thereof. Our metrics depend on two discrete parameters specifying the topology type, as well as $(D-2)(D-3)/2$ continuous parameters. Not all of our metrics in $D \ge 6$ seem to arise as the near horizon limits of known black hole solutions.
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