We present the full set of analytical solutions of the geodesic equations of charged test particles in the Reissner-Nordstr\"om space-time in terms of the Weierstra{} , σ, and ζ elliptic functions. Based on the study of the polynomials in the ϑ and r equations, we characterize the motion of test particles and discuss their properties. The motion of charged test particles in the Reissner-Nordstr\"om space-time is compared with the motion of neutral test particles in the field of a gravitomagnetic monopole. Electrically or magnetically charged particles in the Reissner-Nordstr\"om space-time with magnetic or electric charges, respectively, move on cones similar to neutral test particles in the Taub-NUT space-times.
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Grunau et al. (2011) studied this question.
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