The stability of the recently proposed static solutions for boson stars is analyzed. These solutions of Einstein‐Klein‐Gordon (EKG) equations are obtained by considering the interaction of a real scalar field with matter. We assume that the inclusion of the scalar field in addition to matter allows one 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 scalar field at the origin with the matter energy density at the same point. We also determine the behavior of the total mass with the matter energy density in the origin by obtaining through this and the weak energy condition two possible ranges for stable solutions of static boson stars.

中文翻译：

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静态爱因斯坦·克莱因·戈登·玻色子星的稳定性分析

分析了最近提出的玻色子恒星静态解的稳定性。这些Einstein-Klein-Gordon（EKG）方程的解是通过考虑实数标量场与物质的相互作用而获得的。我们假设除了物质之外还包括标量场，这使人们有理由证明，稳定性意味着当原点处物质密度的初始条件也增加时，溶液的总质量应该增加。根据源与能量密度之间以及此与压力之间的线性关系，利用静态玻色子星的数值，我们发现了将原点上的标量场与同一点上的物质能量密度联系起来的关系。