Some peculiarities of motion of neutral and charged test particles in the field of a spherically symmetric charged object in General Relativity

TL;DR

This paper investigates the radial motion of charged and neutral test particles in the Reissner-Nordström spacetime, classifies their behaviors, and analyzes stability and oscillation frequencies of equilibrium states.

Contribution

It introduces a mass potential method for analyzing particle motion and provides new stability conditions for static equilibrium states in charged black hole fields.

Findings

Stable equilibrium states exist only for weakly charged particles near naked singularities.

Conditions for attraction and repulsion depend on charge signs.

Frequencies of small oscillations around equilibrium are calculated.

Abstract

We propose the method of investigation of radial motions for charged and neutral test particles in the Reissner-Nordstr\"{o}m field by means of mass potential. In this context we analyze special features of interaction of charges and their motions in General Relativity and construct the radial motion classification. For test particles and a central source with charges $q$ and $Q$, respectively, the conditions of attraction (when $qQ>0$) and repulsion (when $qQ<0$) are obtained. The conditions of motionless test particle states with respect to the central source are investigated and, in addition, stability conditions for such static equilibrium states are found. It is shown that stable states are possible only for the bound states of weakly charged particles in the field of a naked singularity. Frequencies of small oscillations of test particles near their equilibrium positions are also found.