A generalization of Hawking's black hole topology theorem to higher dimensions
A generalization of Hawking's black hole topology theorem to higher dimensions
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DOI：
10.1007/s00220-006-0019-z
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发表时间：
2006-09-01
影响因子：
2.4
通讯作者：
Schoen, Richard
中科院分区：
文献类型：
--
作者：
Galloway, Gregory J.;Schoen, Richard
霍金关于黑洞拓扑的定理断言，服从主导能量条件的 4 维渐近平坦静止黑洞时空中事件视界的横截面在拓扑上是 2 球体。这个结论延伸到时空中不一定是静止的外部视界。在本文中，我们通过证明事件视界（在静止情况下）和外视视界（在一般情况下）的横截面是正 Yamabe 类型，即承认正标量曲率的度量，获得了霍金结果到更高维度的自然推广。这意味着对拓扑的许多众所周知的限制，并且与最近具有水平拓扑 S-2 x S-1 的五维静止黑洞时空的例子一致。该证明的灵感来自于 Schoen 和 Yau 之前关于 Jang 方程解存在性的研究（但没有直接使用该方程）。
Hawking's theorem on the topology of black holes asserts that cross sections of the event horizon in 4-dimensional asymptotically flat stationary black hole spacetimes obeying the dominant energy condition are topologically 2-spheres. This conclusion extends to outer apparent horizons in spacetimes that are not necessarily stationary. In this paper we obtain a natural generalization of Hawking's results to higher dimensions by showing that cross sections of the event horizon (in the stationary case) and outer apparent horizons (in the general case) are of positive Yamabe type, i.e., admit metrics of positive scalar curvature. This implies many well-known restrictions on the topology, and is consistent with recent examples of five dimensional stationary black hole spacetimes with horizon topology S-2 x S-1. The proof is inspired by previous work of Schoen and Yau on the existence of solutions to the Jang equation (but does not make direct use of that equation).