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

Abstract

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 $\sigma$-function and in special cases in terms of the Weierstra{\ss} $\wp$-, $\sigma$- and $\zeta$-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.