Tamm-Rubilar分支诊断用于Drummond-Hathrell光子传播：Schwarzschild校准和Kerr弱透镜基准
Tamm-Rubilar branch diagnostics for Drummond-Hathrell photon propagation: Schwarzschild calibration and a Kerr weak-lensing benchmark
AI总结：
本文开发了一种局部Tamm-Rubilar分支诊断方法，用于处理无色散、对偶对称的本构张量，并作为偏振分辨射线传输的预处理层，在Schwarzschild和Kerr时空中验证了其有效性。
AI中文摘要：
本文为提供的无色散、对偶对称的本构张量开发了一种局部Tamm-Rubilar分支诊断方法，并将其用作偏振分辨射线传输的预处理层。该诊断构造了局部四次Fresnel多项式，检查实ADM导向的根和根边界，并将代数分支稳定性与独立的有效场论问题（即Drummond-Hathrell低频替代何时适用）分开。对于具有反射等距的本构张量，适应的双矢量矩阵具有精确的奇偶块形式。全奇偶不变的Tamm-Rubilar多项式是一个四次多项式，其系数在横向动量中为偶，而受限的子午SSSW框架四次多项式仅作为紧凑的解析基准和根边界测试保留。在Schwarzschild中，Ricci平坦的Drummond-Hathrell曲率扇区可分解，并重现了标准的径向无偏移和轨道偏振分裂结果。旋转时空基准是线性化Kerr场中的无穷远到无穷远弱透镜计算。在传输的Born屏幕中，局部慢Kerr磁-Weyl特征基倾斜具有零端点失配，而分支延迟分裂具有与沿透镜平面法线投影的角动量成正比的自旋奇项。对于代表性的紧凑天体掠射光线，由此产生的相位延迟远低于近期可探测性，因此Kerr计算作为诊断和传输框架的可重复尺度设定基准呈现，而非观测主张。
英文摘要：
This paper develops a local Tamm-Rubilar branch diagnostic for supplied nondispersive, pair-symmetric constitutive tensors and uses it as a preprocessing layer for polarization-resolved ray transport. The diagnostic constructs the local quartic Fresnel polynomial, checks real ADM-oriented roots and root margins, and separates algebraic branch stability from the separate effective-field-theory question of when a Drummond-Hathrell low-frequency surrogate is applicable. For constitutive tensors with a reflection isometry, the adapted bivector matrix has an exact parity block form. The full parity-invariant Tamm-Rubilar polynomial is a quartic with coefficients even in the transverse momentum, while a restricted meridional SSSW-frame quartic is retained only as a compact analytic benchmark and root-margin test. In Schwarzschild, the Ricci-flat Drummond-Hathrell curvature sector factorizes and reproduces the standard radial no-shift and orbital polarization-split result. The rotating-spacetime benchmark is an infinity-to-infinity weak-lensing calculation in the linearized Kerr field. In a transported Born screen, the local slow-Kerr magnetic-Weyl eigenbasis tilt has zero leading endpoint mismatch, while the branch-delay split has a spin-odd term proportional to the angular momentum projected along the lens-plane normal. The resulting phase retardance is far below near-term detectability for representative compact-object grazing rays, so the Kerr calculation is presented as a reproducible scale-setting benchmark for the diagnostic and transport framework rather than as an observational claim.
