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arXiv 0903.4723gr-qcmath.DG
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关于荷电黑洞的Hawking局部刚性定理

On Hawking's Local Rigidity Theorems for Charged Black Holes

Pin Yu

摘要:

我们证明了在光滑的爱因斯坦-麦克斯韦时空中,在一个局部的、规则的、分叉的、非扩张的视界的完整邻域中存在霍金矢量场,而不假设基本的时空是解析的。它推广了Friedrich,Rácz和Wald的一个结果,该结果仅限于黑洞区域的内部.此外,我们还证明了,如果存在一个与视界相切且在分叉球面上不为零的Killing矢量场$T$,那么在不作解析性假设的情况下,时空必定是局部轴对称的.这种轴对称性在静止黑洞的分类理论中起着基础性的作用。

英文摘要:

We show the existence of a Hawking vector field in a full neighborhood of a local, regular, bifurcate, non-expanding horizon embedded in a smooth Einstein-Maxwell space-time without assuming the underlying space-time is analytic. It extends one result of Friedrich, Rácz and Wald, which was limited to the interior of the black hole region. Moreover, we also show, in the presence of an additional Killing vector field $T$ which tangent to the horizon and not vanishing on the bifurcate sphere, then space-time must be locally axially symmetric without the analyticity assumption. This axial symmetry plays a fundamental role in the classification theory of stationary black holes.

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