论文标题
固定多轴对称真空黑色孔的几何形状和拓扑
The Geometry and Topology of Stationary Multi-Axisymmetric Vacuum Black Holes in Higher Dimensions
论文作者
论文摘要
在5个维度上进行的最新工作，我们证明了$（n+3）$ - 维度的空间的真空黑洞的解决方案的存在和独特性 - 尺寸的空间时，承认iSometry $ \ mathbb {r} r} \ times times u（r} \ times u（times times u（r} \ times u（1）^n} $ kaluza-kaluza-kaluza-kleiNspt $ nspt for $ n assmpt。这相当于建立单数谐波地图$φ的存在和独特性：\ Mathbb {r}^3 \setMinusγ\ rightArrow sl（n+1，\ mathbb {r}）/so（n+1）$，带有$ z $ - $ - $ - $ - $ - $ - $ - $ - $ - $ - $ - $ - $ - $ s $ s $ z的规定blight。我们还通过对较低维情况中使用的管道结构进行适当的概括来分析这些空间的外部通信领域的拓扑结构。此外，我们为荷兰 - 伊萨巴西（Hollands-Ishibashi）的猜想提供了反例，该猜想是关于外部通信域的拓扑分类。然后，在时空维度小于8的时间内提出并建立了猜想的精致版本。
Extending recent work in 5 dimensions, we prove the existence and uniqueness of solutions to the reduced Einstein equations for vacuum black holes in $(n+3)$-dimensional spacetimes admitting the isometry group $\mathbb{R}\times U(1)^{n}$, with Kaluza-Klein asymptotics for $n\geq3$. This is equivalent to establishing existence and uniqueness for singular harmonic maps $φ: \mathbb{R}^3\setminusΓ\rightarrow SL(n+1,\mathbb{R})/SO(n+1)$ with prescribed blow-up along $Γ$, a subset of the $z$-axis in $\mathbb{R}^3$. We also analyze the topology of the domain of outer communication for these spacetimes, by developing an appropriate generalization of the plumbing construction used in the lower dimensional case. Furthermore, we provide a counterexample to a conjecture of Hollands-Ishibashi concerning the topological classification of the domain of outer communication. A refined version of the conjecture is then presented and established in spacetime dimensions less than 8.
