Geodesic Motion in the (Charged) Doubly Spinning Black Ring Spacetime

In this article we analyze the geodesics of test particles and light in the five-dimensional (charged) doubly spinning black ring spacetime. Apparently it is not possible to separate the Hamilton-Jacobi equation for (charged) doubly spinning black rings in general, so we concentrate on special cases: null geodesics in the ergosphere and geodesics on the two rotational axes of the (charged) doubly spinning black ring. We present analytical solutions to the geodesic equations for these special cases. Using effective potential techniques we study the motion of test particles and light and discuss the corresponding orbits.