Circular motion in Reissner-Nordstr\"om spacetime

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 $r>Q^2/M$.