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 (EVPA) residuals of $\langle \Delta \mathrm{PA} \rangle \approx 0.09^\circ$, a 95th percentile of $0.31^\circ$, and a worst case $\Delta \mathrm{PA} \lesssim 0.32^\circ$ 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 ($\Delta \mathrm{PA} \lesssim 2^\circ$) near the Thorne spin limit. Photon four-momenta $k^\mu$ and polarization four-vectors $f^\mu$ are advanced using a fourth order Runge-Kutta scheme with cached Christoffel symbols, maintaining the constraints $u\cdot f=0$ and $n\cdot f=0$, where $u^\mu$ is the ZAMO four-velocity and $n^\mu$ is the disk normal, while keeping $k\cdot f \simeq 0$. A physically motivated gauge is enforced by projecting the polarization into the local zero-angular-momentum observer (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. The method comfortably meets IXPE and NICER polarization tolerances and approaches EHT requirements. The approach provides a practical foundation for future general relativistic polarimetry and simulation pipelines.