Circular motion of neutral test particles in Reissner-Nordstr\"om spacetime

TL;DR

This paper analyzes the motion of neutral particles in Reissner-Nordström spacetime, revealing unique orbit behaviors near black holes and naked singularities, including zero angular momentum orbits and stability regions.

Contribution

It provides a detailed analysis of circular orbits in RN spacetime, highlighting differences between black holes and naked singularities regarding orbit stability and zero angular momentum.

Findings

Existence of zero angular momentum orbits at classical radius

Black holes have a continuous stable orbit region

Naked singularities have split stable orbit regions

Abstract

We investigate the motion of neutral test particles in the gravitational field of a mass $M$ with charge $Q$ described by the Reissner-Nordstr\"om (RN) spacetime. We focus on the study of circular stable and unstable orbits around configurations describing either black holes or naked singularities. We show that at the classical radius, defined as $Q^2/M$, there exist orbits with zero angular momentum due to the presence of repulsive gravity. The analysis of the stability of circular orbits indicates that black holes are characterized by a continuous region of stability. In the case of naked singularities, the region of stability can split into two non-connected regions inside which test particles move along stable circular orbits.