卡斯纳背景下的引力透镜效应：区分虫洞和黑洞
Gravitational Lensing in a Kasner Background: Distinguishing Wormholes and Black Holes
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中文总结 AI 辅助
研究嵌入各向异性比安奇 - I 宇宙学中致密天体的引力透镜效应，用方向雅可比映射推导相关方程和曲线，表明特征尺度分裂可探各向异性膨胀，临界曲线变形弱，且不同弱场偏转定律对相同背景过滤不同，为解开宇宙学各向异性提供框架。
中文摘要 AI 辅助
我们使用薄透镜近似中的方向雅可比映射，研究嵌入各向异性比安奇 - I 宇宙学中的致密天体的引力透镜效应。该形式体系针对一般对角比安奇 - I 时空发展，并专门应用于卡斯纳解作为易于分析的背景。以埃利斯 - 布龙尼科夫虫洞和史瓦西黑洞作为代表性透镜，我们推导了各向异性透镜方程、特征轴对齐的透镜尺度以及相应的临界曲线。我们表明特征尺度的方向分裂取决于完整的源 - 透镜 - 观测者光学传播，并提供了一个独立于整体透镜尺度的各向异性膨胀的几何探针。相比之下，精确的临界曲线显示出弱得多的变形，表明特征尺度分裂和临界曲线形态探测透镜映射的不同方面。虫洞透镜和黑洞透镜的比较进一步揭示，相同的各向异性背景被不同的弱场偏转定律以不同方式过滤。这些结果为从致密透镜的局部几何结构中解开宇宙学各向异性提供了一个简单框架。
英文摘要
We investigate gravitational lensing by compact objects embedded in anisotropic Bianchi-I cosmologies using directional Jacobi maps within the thin-lens approximation. The formalism is developed for a general diagonal Bianchi-I spacetime and specialized to the Kasner solution as an analytically tractable background. Using the Ellis--Bronnikov wormhole and the Schwarzschild black hole as representative lenses, we derive anisotropic lens equations, characteristic axis-aligned lensing scales, and the corresponding critical curves. We show that the directional splitting of the characteristic scales depends on the complete source--lens--observer optical propagation and provides a geometric probe of anisotropic expansion independent of the overall lens scale. By contrast, the exact critical curves exhibit a much weaker deformation, indicating that characteristic-scale splitting and critical-curve morphology probe distinct aspects of the lens mapping. The comparison between wormhole and black-hole lenses further reveals that identical anisotropic backgrounds are filtered differently by distinct weak-field deflection laws. These results provide a simple framework for disentangling cosmological anisotropy from the local geometry of compact lenses.
