{"title":"Ray tracing through absorbing dielectric media in the Schwarzschild spacetime","authors":"Adam Rogers","doi":"10.1088/1361-6382/ad64a5","DOIUrl":null,"url":null,"abstract":"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 . 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.","PeriodicalId":10282,"journal":{"name":"Classical and Quantum Gravity","volume":null,"pages":null},"PeriodicalIF":3.6000,"publicationDate":"2024-07-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Classical and Quantum Gravity","FirstCategoryId":"101","ListUrlMain":"https://doi.org/10.1088/1361-6382/ad64a5","RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"ASTRONOMY & ASTROPHYSICS","Score":null,"Total":0}
引用次数: 0
Abstract
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 . 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.
广义相对论描述了光线穿过大质量物体附近弯曲时空的轨迹。除了引力透镜之外,我们还加入了由复折射率给出的吸收介质,即德鲁德模型。当吸收被包含在内时,eikonal 变为复数,其虚部与发射点和观测点之间沿射线的吸收有关。我们扩展了文献中的结果,将折射率的色散也包括在内。复数哈密顿方程分为描述运动方程的实部和控制系统动量损失的约束方程。我们的工作坐标是完全实数的,物理时空中有一个实数度量。我们假设德鲁德物质的尘埃和等离子体分布是重合的,并呈幂律变化。我们发现,传输要求 h > 1,否则沿射线路径会发生指数吸收。我们利用光线追踪法穿过紧凑恒星表面附近的强吸收物质,以及在弱场极限中通过弱吸收物质特化到点透镜,为遥远的观测者生成潜在的可观测光曲线。在适当的限度内,我们的理论重现了文献中的结果。
期刊介绍:
Classical and Quantum Gravity is an established journal for physicists, mathematicians and cosmologists in the fields of gravitation and the theory of spacetime. The journal is now the acknowledged world leader in classical relativity and all areas of quantum gravity.