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arXiv 0904.4246hep-thgr-qc
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黑洞时空的畴结构

Domain Structure of Black Hole Space-Times

Troels Harmark

摘要:

我们引入了稳态黑洞时空的畴结构。给定时空的一组交换Killing向量场,域结构存在于至少一个Killing向量场具有零范数的子流形上。根据哪一个Killing向量场具有零范数,子流形自然地被划分为域。一个域对应于一组空间对称的不动点或一个基灵视界,这取决于表征基灵向量场在域附近是类空还是类时。域结构提供了空间-时间的拓扑和几何不变量。它定义为任何时空维度和任何数量的交换Killing向量场。我们研究了渐近平坦时空的域结构,并找到了这种时空度量的标准形。域结构推广了引入D-2交换Killing向量场的时空的棒结构。我们详细分析了Minkowski空间、Schwarzschild-Tangherlini黑洞和Myers-Perry黑洞在六维和七维空间中的畴结构。最后,我们考虑了六维和七维渐近平坦黑洞可能的畴结构。

英文摘要:

We introduce the domain structure for stationary black hole space-times. Given a set of commuting Killing vector fields of the space-time the domain structure lives on the submanifold where at least one of the Killing vector fields have zero norm. Depending on which Killing vector field has zero norm the submanifold is naturally divided into domains. A domain corresponds either to a set of fixed points of a spatial symmetry or to a Killing horizon, depending on whether the characterizing Killing vector field is space-like or time-like near the domain. The domain structure provides invariants of the space-time, both topological and geometrical. It is defined for any space-time dimension and any number of commuting Killing vector fields. We examine the domain structure for asymptotically flat space-times and find a canonical form for the metric of such space-times. The domain structure generalizes the rod structure introduced for space-times with D-2 commuting Killing vector fields. We analyze in detail the domain structure for Minkowski space, the Schwarzschild-Tangherlini black hole and the Myers-Perry black hole in six and seven dimensions. Finally we consider the possible domain structures for asymptotically flat black holes in six and seven dimensions.

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