For Reissner-Nordström naked singularities, each rational periodic orbit in the outer region can share the same energy and angular momentum with an inner-region periodic orbit, and the full (L,E) atlas is divided into distinct root-configuration domains.
Geodesics of electrically and magnetically charged test particles in the Reissner-Nordstr\"om space-time: analytical solutions
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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} $\wp$, $\sigma$ and $\zeta$ elliptic functions. Based on the study of the polynomials in the $\vartheta$ 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.
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Periodic orbits of neutral test particles in Reissner-Nordstr\"{o}m naked singularities
For Reissner-Nordström naked singularities, each rational periodic orbit in the outer region can share the same energy and angular momentum with an inner-region periodic orbit, and the full (L,E) atlas is divided into distinct root-configuration domains.