# Bound orbits near scalar field naked singularities

## TL;DR

This paper investigates the properties of bound orbits near scalar field configurations, including naked singularities and black holes, revealing unique orbital features such as static degenerate orbits and negative precession angles.

## Contribution

It provides a detailed analysis of bound orbits around scalar field naked singularities and black holes, highlighting novel orbital behaviors and potential observational signatures.

## Key findings

- Scalar field naked singularities have a static degenerate orbit at zero angular momentum.
- Bound orbits near SFNSs can form a spherical shell resembling a black hole shadow.
- Noncircular orbits exhibit negative precession angles.

## Abstract

We study bound orbits near the centres of static, spherically symmetric, asymptotically flat configurations of a self-gravitating scalar field minimally coupled to gravity. In our approach, a nonlinear scalar field is considered as an idealized model of dark matter, and the main examples that we have in mind are the centres of galaxies. We consider both scalar field black holes (SFBHs) and scalar field naked singularities (SFNSs). It turns out that the shape and parameters of a bound orbit depend crucially on the type of configuration. The lapse metric function of a SFNS and, consequently, the effective potential of a massive test particle with zero angular momentum have a global minimum. A SFNS has a static degenerated orbit on which a test particle, having zero angular momentum and the minimum of its energy, remains at rest at all times. This implies that there exists a spherical shell consisting of cold gas or dust, which for a distant observer can look like the shadow of a black hole. We also study the shape of noncircular bound orbits close to the centres of SFNSs and show that their angles of precession are negative.