The mass of dark scalar and phase space analysis of realistic models of static spherically symmetric objects

TL;DR

This paper analyzes the singularities and phase space structure of static spherically symmetric objects in minimal dilatonic gravity, introducing a Lyapunov function to understand stability and the influence of dark scalar mass.

Contribution

It provides a comprehensive classification of singularities and introduces a novel Lyapunov function for the system, enhancing understanding of stability in extended gravity models.

Findings

Classification of singularities into sub-manifolds of phase space

Introduction of a Lyapunov function for the system

Discussion of dark scalar mass effects on solutions

Abstract

We consider singularities of static spherically symmetric objects in minimal dilatonic gravity. They are only partially studied and purely understood even in the simplest models of extended gravity. We introduce the proper form of the structure equations and derive a set of all singularities, which turn to form several types of sub-manifolds of the phase space. We also introduce for the first time the Lyapunov function for the corresponding system, its equation, and its basic properties. The dependence on the mass of the dark scalar is discussed.