稳态黑洞中至多存在一个内部 Killing 视界
At Most One Inner Killing Horizon in Stationary Black Holes
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中文总结 AI 辅助
本文证明满足经典能量条件的稳态轴对称黑洞在每个内部分支至多有一个内部Killing视界，通过能量条件与几何流揭示引力聚焦机制的双重作用。
中文摘要 AI 辅助
稳态轴对称黑洞是天体物理黑洞的标准理论框架，然而其内部在很大程度上仍难以探测：由于不存在超曲面正交的类时 Killing 矢量，度规变为非对角的，而参考系拖曳效应阻碍了通常用于探测内部的技术。我们证明，任何满足经典能量条件的稳态轴对称黑洞，在每个连通的内部分支中至多包含一个非退化的内部 Killing 视界，无论其物质内容如何。对于紧致的视界截面，我们将 Raychaudhuri 方程应用于常时超曲面的法向汇：强能量条件使得平方时移函数为次调和函数，最大值原理排除了第二个内部视界的存在。对于在全息中至关重要的非紧致平面和双曲截面，零能量条件则通过我们在此引入的一种几何流——"逆时移流"——产生单调性阻碍，我们还通过粘性解构造了该流的弱延拓。引力的吸引性质（编码在这些能量条件中）既驱动视界的形成，又限制了内部视界的数量，揭示了同一聚焦机制的显著双重作用。
英文摘要
Stationary-axisymmetric black holes are the standard theoretical framework for astrophysical black holes, yet their interiors remain largely inaccessible: the absence of a hypersurface-orthogonal timelike Killing vector renders the metric non-diagonal, and frame dragging obstructs the usual techniques for probing the interior. We prove that any stationary-axisymmetric black hole satisfying the classical energy conditions contains at most one nondegenerate inner Killing horizon per connected interior branch, irrespective of its matter content. For compact horizon sections, we apply the Raychaudhuri equation to the congruence normal to constant-time hypersurfaces: the strong energy condition makes the squared lapse subharmonic, and the maximum principle excludes a second inner horizon. For noncompact planar and hyperbolic sections central to holography, the null energy condition instead yields a monotonicity obstruction through a geometric flow we introduce here, the ``inverse lapse flow,'' whose weak continuation via viscosity solutions we also construct. The attractive nature of gravity, encoded in these energy conditions, thus both drives horizon formation and caps the number of inner horizons, revealing a striking dual role of the same focusing mechanism.
发表机构
- Tianjin University（天津大学）
- Institute of Theoretical Physics, Chinese Academy of Sciences（中国科学院理论物理研究所）
- University of Chinese Academy of Sciences（中国科学院大学）
- Hangzhou Institute for Advanced Study, UCAS（杭州高等研究院，中国科学院大学）
机构由 AI 辅助整理，请以论文原文为准。
