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Fast and accurate integration of geodesics in Kerr spacetimes is an importanttool in modeling the orbits of stars and the transport of radiation in thevicinities of black holes. Most existing integration algorithms employBoyer-Lindquist coordinates, which have coordinate singularities at the eventhorizon and along the poles. Handling the singularities requires specialnumerical treatment in these regions, often slows down the calculations, andmay lead to inaccurate geodesics. We present here a new general-purposegeodesic integrator, GRay2, that overcomes these issues by employing theCartesian form of Kerr-Schild coordinates. By performing particularmathematical manipulations of the geodesic equations and several optimizations,we develop an implementation of the Cartesian Kerr-Schild coordinates thatoutperforms calculations that use the seemingly simpler equations inBoyer-Lindquist coordinates. We also employ the OpenCL framework, which allowsGRay2 to run on multi-core CPUs as well as on a wide range of GPU hardwareaccelerators, making the algorithm more versatile. We report numerousconvergence tests and benchmark results for GRay2 for both time-like (particle)and null (photon) geodesics.

GRay2: A General Purpose Geodesic Integrator for Kerr Spacetimes