Comparing Numerical Ray Tracing Methods in the Presence of Strong Gravitational Lensing

In this talk, we compare the performance of various numerical methods for ray tracing in the presence of a strong gravitational lens. Specifically, we highlight the shortcomings of the popular fourth-order Runge-Kutta method and propose a more suitable selection of alternative methods. We place particular emphasis on symplectic numerical methods, which have historically been a mainstay of molecular dynamics simulations and are now becoming popular for ray tracing. To demonstrate the utility of symplectic methods, we place a source of rays near a Schwarzschild black hole, where significant discrepancies arise in the ray trajectories traced by the symplectic and nonsymplectic methods. Ultimately, we hope this result will inform technosignature searches in the vicinity of strong gravitational lenses, such as black holes found in galactic centers.