发表机构
Simion Stoilow Institute of Mathematics, Romanian Academy（罗马尼亚科学院西米恩·斯托伊洛数学研究所）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文证明具有足够小ADM角动量的光滑渐近平坦稳态真空黑洞满足全局刚性，通过变换为爱因斯坦-麦克斯韦族并利用面积-电荷不等式，最终恢复Kerr度量并给出视界估计。
AI 中文摘要
我们证明了在全局正则性、分叉和极大超曲面假设下，具有足够小ADM角动量的光滑渐近平坦稳态真空黑洞的全局刚性，其阈值依赖于固定的几何界。这回答了Alexakis、Ionescu和Klainerman关于用无穷远处角动量的小性替代他们在分叉球面上稳态场小性假设的问题。主要步骤建立了任意角动量下Kerr黑洞在无穷远处的刚性。我们将真空度量变换为爱因斯坦-麦克斯韦族，并比较其极限端的零聚焦与紧致极大超曲面上的面积-电荷不等式，该超曲面通过族中的延拓构造。等式同时确定了变换后的度量及其稳态场，逆变换由此恢复Kerr度量。两个Kerr恒等式随后给出全局结论所需的视界估计。
英文摘要
We prove global rigidity of smooth asymptotically flat stationary vacuum black holes with sufficiently small ADM angular momentum, under global regularity, bifurcation, and maximal-hypersurface assumptions, with a threshold depending on fixed geometric bounds. This answers the question of Alexakis, Ionescu, and Klainerman concerning replacement of their smallness assumption on the stationary field at the bifurcation sphere by smallness of the angular momentum at infinity. The main step establishes Kerr rigidity near infinity for arbitrary angular momentum. We transform the vacuum metric into an Einstein--Maxwell family and compare null focusing at its limiting end with the area--charge inequality on compact maximal hypersurfaces, constructed by continuation through the family. Equality determines both the transformed metric and its stationary field, from which the inverse transformation recovers Kerr. Two Kerr identities then give the horizon estimate required for the global conclusion.
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