具有完整渐近喉部的黑洞

中文摘要 AI 辅助

我们研究了一个球对称黑洞是否可以在有限、非零的视界半径处具有完整的内端，同时在其视界外部足够远处满足标准能量条件。保留两个独立的度规函数，我们同时处理类空型和类光型渐近喉部，并推导出因果测地线完整性的一个充要积分判据。在独立曲率分量有界且具有有限极限的假设下，类光型端部的极限曲率由喉部半径固定，而类空型端部则允许一个额外的非负曲率参数。我们获得了在类时和类光平行传播标架中曲率有界的判据。完整的类空型例子可以具有有界的标量不变量和有界的类时标架曲率，但在无限仿射参数处具有无界的类光标架曲率。我们还证明了，在所陈述的类别中，径向类光能量条件必须在每个完整内端附近任意近处失效。然而，具有任一种喉部的显式实解析构造在足够远的外部区域中满足类光、弱、主和强能量条件。光滑构造可以在有限半径之外精确地变为史瓦西形式。这些结果确立了完整渐近喉部与外部能量条件的相容性，同时将完整性与不同水平的曲率正则性区分开来。

英文摘要

We investigate whether a spherically symmetric black hole can have a complete inner end at finite, nonzero areal radius while satisfying the standard energy conditions sufficiently far outside its horizon. Retaining two independent metric functions, we treat both null-type and spacelike-type asymptotic throats and derive a necessary and sufficient integral criterion for causal geodesic completeness. Under boundedness and finite-limit assumptions on the independent curvature components, null-type ends have limiting curvature fixed by the throat radius, whereas spacelike-type ends admit an additional nonnegative curvature parameter. We obtain criteria for bounded curvature in timelike and null parallel-propagated frames. Complete spacelike-type examples can have bounded scalar invariants and bounded timelike-frame curvature but unbounded null-frame curvature at infinite affine parameter. We also prove that the radial null energy condition must fail arbitrarily close to every complete inner end in the stated class. Nevertheless, explicit real-analytic constructions with either type of throat satisfy the null, weak, dominant, and strong energy conditions throughout a sufficiently distant exterior region. Smooth constructions can become exactly Schwarzschild beyond a finite radius. These results establish the compatibility of complete asymptotic throats with exterior energy conditions while distinguishing completeness from different levels of curvature regularity.

发表机构

• School of Physics, Xi’an Jiaotong University（西安交通大学物理学院）

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