Geodesics of electrically and magnetically charged test particles in the Reissner-Nordstr\"om space-time: analytical solutions

TL;DR

This paper derives exact analytical solutions for the trajectories of charged test particles in Reissner-Nordström space-time using elliptic functions, revealing their motion characteristics and similarities to other space-times.

Contribution

It provides the first complete analytical solutions of charged particle geodesics in Reissner-Nordström space-time using elliptic functions, characterizing their motion.

Findings

Charged particles move on conical trajectories similar to those in Taub-NUT space-time.

Analytical solutions are expressed in terms of Weierstraß elliptic functions.

The study compares charged and neutral particle motions in different gravitational fields.

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} $\wp$, $\sigma$ 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.