Geodesics of electrically and magnetically charged test particles in the Reissner-Nordström space-time: Analytical solutions

Abstract

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\ss{} $\ensuremath{\wp}$, $\ensuremath{\sigma}$, and $\ensuremath{\zeta}$ elliptic functions. Based on the study of the polynomials in the $\ensuremath{\vartheta}$ 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.