Kerr Polarization Transport: Accuracy and Performance in General Relativistic Light Propagation

Abstract We present a compact and reproducible method for general-relativistic polarization transport in the Kerr metric that achieves median electric-vector position-angle residuals of 〈ΔPA〉 ≈ 0 . ° 09, a 95th percentile of 0 . ° 31, and a worst-case ΔPA ≲ 0 . ° 32 for spins up to ∣ a / M ∣ = 0.9, while maintaining a fivefold or greater speedup relative to a strict reference integrator. Across the benchmark grid, typical residuals remain at the sub-tenth-degree level, with only modest degradation (ΔPA ≲ 2 ∘ ) near the Thorne spin limit. Photon four-momenta k μ and polarization four-vectors f μ are advanced using a fourth-order Runge–Kutta scheme with cached Christoffel symbols, maintaining the orthogonality constraints w · f = 0 and n · f = 0, where w μ is the zero-angular-momentum observer (ZAMO) four-velocity and n μ is the disk normal, while preserving k · f = 0 to numerical precision. A physically motivated gauge is enforced by projecting the polarization into the local ZAMO screen at every substep, ensuring numerical stability of the orthogonality constraints. Accuracy and performance are benchmarked over a representative grid in spin, inclination, image-plane azimuth, and radius. In this initial implementation, we restrict photon propagation to the equatorial plane ( θ = π /2) in order to isolate the performance of the transport integrator. The achieved numerical accuracy is substantially smaller than the published statistical uncertainties of current X-ray polarimetric measurements of Cygnus X-1 obtained with the Imaging X-ray Polarimetry Explorer (IXPE). This indicates that the method is well suited for contemporary relativistic polarimetry at the level of present IXPE statistical precision.