Tamm-Rubilar branch diagnostics for Drummond-Hathrell photon propagation: Schwarzschild calibration and a Kerr weak-lensing benchmark

Abstract

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.

27 pages, 1 figure, 1 table. Major replacement of arXiv:2603.21352v1-v2: title and scope changed; prior ansatz-dependent warp-drive screening claim removed as a main result and retained only as an appendix-level test. Refocused on Tamm-Rubilar diagnostics, DH calibration, and Kerr weak-lensing. Ancillary code bundle included