Periodic orbits of neutral test particles in Reissner–Nordström naked singularities

Abstract

We conduct studies on Levin’s taxonomy of periodic orbits for neutral test particles around a Reissner-Nordström naked singularity. It was known that naked singularities could harbor two distinct regions of time-like bound orbits and thus we expect periodic orbits to appear in both regions. It is possible for a pair of periodic orbits from both regions to possess the exact same angular momentum L and energy E values. We chart the sets of periodic orbits in (L, E)-parameter space and highlight the general distribution pattern of these sets for three possible scenarios. Regions within (L, E)-space can be partitioned into multiple domains \({\mathcal {D}}_k\) based on the roots configuration of the quartic polynomial P(u) where u is the inverse radial coordinate. Consequently, each domain and interestingly enough, portions of certain periodic orbits sets that lie in different \({\mathcal {D}}_k\) require different analytical solutions to plot the resulting orbit. Furthermore, we uncover physical properties of some hypothetical circular orbits residing in the inner region from analysing the (L, E)-space.