发表机构
Simion Stoilow Institute of Mathematics, Romanian Academy（罗马尼亚科学院西蒙·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
本文证明在无陷获假设下，光滑渐近平坦静止真空黑洞外部必为极端Kerr解，通过区域延拓和零测地线分析建立全局轴对称性。
AI 中文摘要
我们证明，一个光滑、正则、渐近平坦的静止真空黑洞，若没有正交于其静止Killing场的零测地线被陷获，则其外部必为极端Kerr外部。我们通过选取连续区域来扩展局部旋转对称性，这些区域在能量区中的极限边界（若非空）局部上是静止商度规的类时光子面。为了在没有初始边界正则性假设的情况下获得该几何，我们从无陷获性出发沿完整旋转轨道推导一致估计，并利用短零线段上的凸性来控制边界。其零测地线提升为时空零测地线，且正交于静止场。圆性允许我们通过能量面接触继续延伸它们，此时静止投影限于紧集，这与无陷获性矛盾，从而得到全局轴对称性。
英文摘要
We prove that a smooth, regular, asymptotically flat stationary vacuum black hole has a nonextremal Kerr exterior if no null geodesic orthogonal to its stationary Killing field is trapped, establishing the rigidity conjecture of Alexakis, Ionescu, and Klainerman. In the rotating case, we start with the rotational Killing field constructed near the bifurcation sphere and study a maximal domain carrying its complete circle action. The main difficulty is to recover boundary regularity and the curvature condition needed for local Killing extension. We derive uniform estimates along complete rotational orbits from nontrapping and combine them with convexity along short null geodesics. These estimates show that a nonempty remaining boundary in the ergoregion is a timelike photon surface for the stationary quotient metric. Its null geodesics lift to spacetime null geodesics orthogonal to the stationary field. The vacuum circularity identities give their continuation through contact with the ergosurface, keeping their stationary projections in a compact set. This contradicts nontrapping and yields the global rotational symmetry required by black hole uniqueness.
Comments76 pg, 6 figures, improved presentation
