# Spherically symmetric configurations of General Relativity in presence of scalar field: separation of test body circular orbits

## TL;DR

This paper analyzes test-body circular orbits around spherically symmetric objects influenced by scalar fields, revealing conditions for separated stable orbit regions around black holes and naked singularities, with implications for dark energy models.

## Contribution

It provides an analytic family of solutions for scalar field configurations affecting orbits, identifying conditions for separated stable orbit regions around black holes and naked singularities.

## Key findings

- Separated stable orbit regions can exist around both black holes and naked singularities.
- Analytic solutions are expressed via hypergeometric functions for a two-parameter scalar field family.
- Conditions for the existence of separated orbit regions are established.

## Abstract

We study test-body orbits in the gravitational field of a static spherically symmetric object in presence of a minimally coupled nonlinear scalar field. We generated a two-parametric family of scalar field potentials, which allow finding solutions of Einstein's equations in an analytic form. The results are presented by means of hypergeometric functions; they describe either a naked singularity (NS) or a black hole (BH). Our numerical investigation shows that in both cases the stable circular orbits can form separated (non-connected) regions around the configuration. We found existence conditions for such separated regions and present examples for some family parameters in case of NS and BH. The results may be of interest for testing models of the dynamical dark energy.