Photon Bending, Extreme Anisotropic Refraction, and Polarized X-Ray Signatures at Magnetar Poles via Maxwell-Oldroyd-B Vacuum Electrodynamics

Abstract The propagation of light in strong gravitational and magnetic fields is a cornerstone for testing theories of fundamental physics. Standard General Relativity coupled with Euler-Heisenberg QED effective actions accounts for vacuum birefringence and photon splitting near magnetars; however, these frameworks still rely on geometric curvature and virtual particle loop corrections in an otherwise empty topological void. Within the Dynamic Substrate Theory (DST), the vacuum is reframed as a physical, compressible viscoelastic medium governed by Maxwell-Oldroyd-B rheology. In this work, we present the mathematical framework for calculating polar photon bending and polarization signatures under this paradigm, demonstrating how colossal magnetic fields (B \ge 10^{14}\text{ G}) intensely strain the substrate matrix, alter local refractive index tensors, and produce distinct observational signatures testable via advanced X-ray polarimetry. Keywords: Magnetar Electrodynamics, Maxwell-Oldroyd-B Vacuum, Anisotropic Refraction, Photon Bending, Vacuum Viscoelasticity, Dynamic Substrate Theory.