非度量性迹形式与弱场光线偏折：一种几何光学表述
Non-Metricity Trace Forms and Weak-Field Light Deflection: A Geometric Optical Formulation
- Department of Physics, Pamukkale University（帕姆卡莱大学物理系）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
本文提出一种弱场非度量性几何光学框架，通过非度量性迹形式直接推导有效折射率与光线偏折角，无需微观形变假设，给出与爱丁顿一致的偏折结果。
AI中文摘要：
本文发展了一种弱场、非度量的引力光线偏折的操作性描述。在史瓦西弱场的各向同性表述中，非度量性迹1-形式W和P被显式计算，并表明它们通过精确关系$d\ln n=W-4P$（其中$n=g/f$）决定光学响应。因此，控制零传播的有效折射率并非作为外部光学类比引入，而是直接与非度量性的迹扇区相联系。为了将迹几何与物质联系起来，一个有效的标量校准势$\chi$由观测者投影的宏观膨胀流驱动，在静态弱场极限下得到$\nabla^2\chi=-\kappa\rho$。点质量校准确定$\Phi=\chi/C_0\simeq 2GM/(rc^2)$，由此得到的光学计算给出爱丁顿偏折角$4GM/(bc^2)$。该结果的意义不在于修正数值预测，而在于建立了一条从宏观膨胀源到非度量性迹、有效折射率以及光线偏折的闭合弱场链，无需假设材料杆或钟的微观形变定律。
英文摘要：
This paper develops a weak-field, non-metric operational account of gravitational light deflection. In the isotropic formulation of the Schwarzschild weak field, the non-metricity trace 1-forms W and P are computed explicitly and shown to determine the optical response through the exact relation $d\ln n=W-4P$, $n=g/f$. Thus the effective refractive index governing null propagation is not introduced as an external optical analogy, but is tied directly to the trace sector of non-metricity. To connect the trace geometry with matter, an effective scalar calibration potential $χ$ is sourced by an observer-projected macroscopic dilation current, yielding $\nabla^2χ=-κρ$ in the static weak-field limit. The point-mass calibration fixes $Φ=χ/C_0\simeq 2GM/(rc^2)$, and the resulting optical calculation gives the Eddington deflection angle $4GM/(bc^2)$. The significance of the result is not a modified numerical prediction, but a closed weak-field chain from macroscopic dilation sourcing to non-metricity traces, effective refractive index, and light deflection, without postulating a microscopic deformation law for material rods or clocks.
