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The null geodesic equation in the Kerr spacetime can be expressed as a set ofintegral equations involving certain potentials. We classify the roots of thesepotentials and express the integrals in manifestly real Legendre elliptic form.We then solve the equations using Jacobi elliptic functions, providing thecomplete set of null geodesics of the Kerr exterior as explicit parameterizedcurves.

The Null Geodesics of the Kerr Exterior