A stability analysis of the static EKG Boson Stars

TL;DR

This paper investigates the stability of static boson star solutions derived from Einstein-Klein-Gordon equations, linking scalar field behavior and matter density to stability criteria through numerical analysis.

Contribution

It introduces a stability analysis framework for static boson stars considering scalar-matter interactions and derives conditions for stability based on total mass and matter density relations.

Findings

Identified a relation between scalar field at the origin and matter energy density.

Determined the behavior of total mass with respect to matter density.

Established two possible ranges for stable solutions based on energy conditions.

Abstract

The stability of the recently proposed static solutions for boson stars is analyzed. These solutions of Einstein-Klein-Gordon (EKG) equations arise from considering the interaction of a real scalar field with matter. We assume that the inclusion of the scalar field in addition with matter, allows to justify that stability implies that the total mass of the solution should grow when the initial condition for the density of matter at the origin is also increased. Employing numerical values for the static boson star based on a linear relation between the source and the energy density and between this and the pressure, we found the relation that linked the the scalar field at the origin with the matter energy density (MED) in the same point. We also determine the behavior of the total mass (TM) with the matter energy density in the origin, by also obtaining through this and the weak energy condition, two possible ranges for stable solutions of static boson stars.