本文在广义相对论框架下，通过引入复折射率的 Drude 模型研究 Schwarzschild 时空中的吸收性介电介质光线追踪，推导出包含色散的复 Hamilton 量与动量损失约束方程，并生成了可观测的光变曲线。
摘要：
广义相对论描述了光线在大质量物体附近弯曲时空中传播的轨迹。除了引力透镜效应外，我们引入了由复折射率（即 Drude 模型）描述的吸收性介电介质。当考虑吸收效应时，程函变为复数，其虚部与发射点和观测点之间光线沿路径的吸收有关。我们扩展了文献中的结果，将折射率的色散纳入考量。复 Hamilton 量分为描述运动方程的实部和约束系统动量损失的约束方程。我们在完全实数的坐标系下工作，物理时空中具有实度规。我们假设 Drude 物质的尘埃和等离子体分布重合，且按幂律 $1/r^h$ 变化。我们发现透射要求 $h>1$，否则光线沿路径会发生指数吸收。我们通过对致密星表面附近的强吸收物质进行光线追踪，并在弱场极限下针对点透镜及弱吸收物质进行特化处理，为遥远的观测者生成可能可观测的光变曲线。在适当的极限下，我们的理论重现了文献中的结果。
英文摘要：
General Relativity describes the trajectories of light-rays through curved spacetime near a massive object. In addition to gravitational lensing, we include an absorbing dielectric medium given by a complex refractive index known as the Drude model. When absorption is included the eikonal becomes complex, with the imaginary part related to the absorption along a ray between emission and observation points. We extend results from the literature to include dispersion in the index of refraction. The complex Hamiltonian splits into a real part that describes the equations of motion and a constraint equation that governs the momentum loss in the system. We work in coordinates which are fully real, with a real metric in physical spacetime. We assume the dust and plasma distributions of the Drude matter to coincide and vary as a power-law $1/r^h$. We find that transmission requires $h>1$, otherwise exponential absorption occurs along ray paths. We use ray-tracing through strongly absorbing matter near the surface of the compact star, as well as specializing to a point-lens in the weak-field limit with weakly absorbing matter to generate potentially observable light curves for distant observers. In the appropriate limits, our theory reproduces results from the literature.
Seeing relativity -- I. Ray tracing in a Schwarzschild metric to explore the maximal analytic extension of the metric and making a proper rendering of the stars
Optical Signatures of a Schwarzschild Black Hole in a Dehnen-Type Dark Matter Halo
Institute of Fundamental and Applied Research, National Research University TIIAME（基础与应用研究所，国立研究大学TIIAME）；National Pedagogical University of Uzbekistan named after Nizami（以尼扎米命名的乌兹别克斯坦国立师范大学）；School of Advanced Sciences, Vellore Institute of Technology（韦洛尔技术学院高等科学学院）；University of Tashkent for Applied Sciences（塔什干应用科学大学）；Tashkent State Technical University（塔什干国立技术大学）；School of Physics, Harbin Institute of Technology（哈尔滨工业大学物理学院）；Institute for Advanced Studies, New Uzbekistan University（新乌兹别克斯坦大学高级研究院）；Institute of Theoretical Physics, National University of Uzbekistan（乌兹别克斯坦国立大学理论物理研究所）
An analytic model for a total process of gravitational collapse: From star to Schwarzschild black hole
RIKEN（理化学研究所）；Yukawa Institute for Theoretical Physics, Kyoto University（京都大学汤川理论物理研究所）；Silesian University in Opava（奥帕瓦西里西亚大学）；Universidad de Tarapacá（塔拉帕卡大学）
Imaging Signatures of the Israel Junction: Photon Ring Evolution in Dynamical Thin Shell Schwarzschild Spacetimes
Peng Huanwu Center for Fundamental Theory（彭桓武理论物理中心）；Department of Modern Physics, University of Science and Technology of China（中国科学技术大学近代物理系）；Institute of Fundamental Physics and Quantum Technology, Department of Physics, School of Physical Science and Technology, Ningbo University（宁波大学物理科学与技术学院物理系基础物理与量子技术研究所）
Magnetic Modification of Black Hole Photospheres with Image Contraction, Efficiency Shifts and Redshift Boosts in Schwarzschild-Bertotti-Robinson Spacetime
Institute of Fundamental and Applied Research, National Research University TIIAME（国立研究大学TIIAME基础与应用研究所）；School of Advanced Sciences, Vellore Institute of Technology（维洛尔理工学院高级科学学院）；University of Tashkent for Applied Sciences（塔什干应用科学大学）；Tashkent State Technical University（塔什干国立技术大学）
Entanglement degradation in regular and singular spacetimes
School of Science and Technology, University of Camerino（卡梅里诺大学理学院）；Istituto Nazionale di Fisica Nucleare (INFN), Sezione di Perugia（意大利国家核物理研究所佩鲁伽分部）；Department of Nanoscale Science and Engineering, University at Albany SUNY（纽约州立大学奥尔巴尼分校纳米科学与工程系）；INAF - Osservatorio Astronomico di Brera（意大利国家天体物理研究所布雷拉天文台）；Al-Farabi Kazakh National University（阿尔法拉比哈萨克国立大学）
Thin accretion-disc transfer functions in the q-metric spacetime: quadrupolar lensing signatures
Al-Farabi Kazakh National University（阿尔法拉比哈萨克国立大学）；Kazakh National Women’s Teacher Training University（哈萨克国立女子师范大学）；Universidad Nacional Autónoma de México（墨西哥国立自治大学）；Università di Roma “La Sapienza”（罗马第一大学）
