A Fast New Public Code for Computing Photon Orbits in a Kerr Spacetime

Relativistic radiative transfer problems require the calculation of photon trajectories in curved spacetime. We present a novel technique for rapid and accurate calculation of null geodesics in the Kerr metric. The equations of motion from the Hamilton–Jacobi equation are reduced directly to Carlson's elliptic integrals, simplifying algebraic manipulations and allowing all coordinates to be computed semianalytically for the first time. We discuss the method, its implementation in a freely available FORTRAN code, and its application to toy problems from the literature.