Periodic orbits around a spherically symmetric naked singularity

TL;DR

This paper investigates the motion of particles around a naked singularity in F/JNW spacetime, analyzing stable orbits, potential barriers, and periodic orbits, revealing differences from black hole scenarios.

Contribution

It provides a detailed analysis of geodesic motion and periodic orbits in F/JNW spacetime, highlighting how scalar fields influence particle trajectories compared to Schwarzschild black holes.

Findings

Particles with angular momentum face infinite barriers for .5</2, preventing approach to the singularity.

Stable and bound circular orbits are characterized and calculated.

Periodic orbits require lower energies than in Schwarzschild spacetime.

Abstract

The motion of time-like test particles in the Fisher/Janis-Newman-Winicour (F/JNW) spacetime is studied with the Hamiltonian formulation of the geodesic equations. The spacetime is characterised by its mass parameter $r_g$ and scalar field parameter $\nu$. The innermost bound and stable circular orbits are calculated and the effective potential is analysed. Consistent with numerical results in earlier literature, for $\nu<1/2$, particles with non-zero angular momentum encounter an infinite potential barrier, preventing them from reaching the naked singularity at $r=r_g$. Periodic orbits in the spacetime are also obtained. Compared to the periodic orbits around the Schwarzschild black hole, it is found that typically lower energies are required for the same orbits in the F/JNW spacetime.