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-Nordström space-time in terms of the Weierstraß $\wp$, $\sigma$ 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-Nordström 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-Nordström 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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• Complete analytic solution of the geodesic equation in Schwarzschild--(anti) de Sitter space--times
• Analytic solutions of the geodesic equation in higher dimensional static spherically symmetric space-times
• Analytic treatment of complete and incomplete geodesics in Taub-NUT space-times

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