Analytic solutions of the geodesic equation for U(1)^2 dyonic rotating black holes

In this article we derive the geodesic equations in the $\text{U(1)}^2$ dyonic rotating black hole spacetime. We present their solutions in terms of the Kleinian $σ$-function and in special cases in terms of the Weierstraß $\wp$-, $σ$- and $ζ$-functions. To give a list of all possible orbits, we analyse the geodesic motion of test particles and light using parametric diagrams and effective potentials.

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