Circular motion in Reissner-Nordstr\"om spacetime

TL;DR

This paper analyzes the properties of neutral test particle circular orbits in Reissner-Nordstr"om spacetime, revealing how orbit stability varies with charge-to-mass ratio and distinguishing between black hole and naked singularity cases.

Contribution

It provides a detailed comparison of circular orbit stability in Reissner-Nordstr"om black holes and naked singularities, highlighting the critical radius and stability regions based on charge-to-mass ratio.

Findings

No circular orbits exist for r<Q^2/M in naked singularities.

Multiple stability regions depend on the Q/M ratio.

All circular orbits are stable for Q/M > √5/2 and r > Q^2/M.

Abstract

We study the motion of neutral test particles along circular orbits in the Reissner-Nordstr\"om spacetime. We use the method of the effective potential with the constants of motion associated to the underlying Killing symmetries. A comparison between the black hole and naked singularity cases is performed. In particular we find that in the naked singularity case for $r<Q^2/M$ no circular orbits can exist, this radius plays a fundamental role in the physics of the naked singularity. For $r>Q^2/M$ and $1<Q/M<\sqrt{9/8}$ there are two stability regions together with a region where all the circular orbits are instable and a zone in which all trajectory are possible but not circular orbits, for $\sqrt{9/8}<Q/M<\sqrt{5}/2$ one stability region and a region where all circular orbits are instable appear, finally for $Q/M>\sqrt{5}/2$ there are all stable circular orbits for $r>Q^2/M$.