On the uniqueness of extremal vacuum black holes
On the uniqueness of extremal vacuum black holes
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论极真空黑洞的独特性
DOI：
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发表时间：
2009
期刊：
影响因子：
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通讯作者：
James Lucietti
中科院分区：
文献类型：
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作者：
P. Figueras;James Lucietti
我们证明了在四维和五维空间中，分别具有一个和两个交换旋转Killing场的渐近平坦的、平稳的、极值的、真空黑洞解的唯一性定理。在非极值情况下，这些问题可以转换为二维轨道空间上的边值问题。我们证明了具有一个极端视界的解的轨道空间同胚于无限条，其中两个边界对应于旋转轴，两个渐进区域对应于空间无穷大和近视界几何。在四维空间中，这使我们能够在渐近平坦的、静止的、旋转的、具有单个极值视界的真空黑洞中建立极值克尔的唯一性。在五维空间中，我们证明了最多存在一个渐进平坦、静止、极端真空黑洞，该黑洞具有连通视界、两个可交换旋转对称性以及给定的区间结构和角动量。我们还提供了具有上述对称性的四维和五维渐近平坦真空黑洞是静态的必要和充分条件（对极值，非极值甚至非连通视界有效）。
We prove uniqueness theorems for asymptotically flat, stationary, extremal, vacuum black hole solutions, in four and five dimensions with one and two commuting rotational Killing fields respectively. As in the non-extremal case, these problems may be cast as boundary value problems on the two-dimensional orbit space. We show that the orbit space for solutions with one extremal horizon is homeomorphic to an infinite strip, where the two boundaries correspond to the rotational axes, and the two asymptotic regions correspond to spatial infinity and the near-horizon geometry. In four dimensions, this allows us to establish the uniqueness of extremal Kerr amongst asymptotically flat, stationary, rotating, vacuum black holes with a single extremal horizon. In five dimensions, we show that there is at most one asymptotically flat, stationary, extremal vacuum black hole with a connected horizon, two commuting rotational symmetries and given interval structure and angular momenta. We also provide necessary and sufficient conditions for four- and five-dimensional asymptotically flat vacuum black holes with the above symmetries to be static (valid for extremal, non-extremal and even non-connected horizons).