In the description of neutron stars, it is very important to consider gravitational theories as general relativity, due to the determining influence on the behavior of the different types of stars, since some objects show densities even bigger than nuclear density. This paper starts with Einstein’s equations for a perfect fluid and then we present a uniparametric stellar model which allows to describe compact objects like neutron stars with compactness ratio u ≤ 0.2533053. The pressure and density are monotone decreasing regular functions, the speed of sound satisfies the causality condition, while the value for its adiabatic index γ = 4.9227102 > 4/3 guarantees the stability. In addition, the graph of P versus ρ shows a quasi-linear relationship for the equation of state P(ρ) = Pc(ρ − ρb)/(ρc − ρb), which is similar to the so-called MIT Bag equation when we have the interaction between quarks. In our case it is due to the interaction of the different components found inside the star, such as electrons and neutrons. As an application of the model, we describe the star PSR J1614-2230 with a observed mass of M = (1.97 ± 0.04)M⊙ and a radius R = (13 ± 2)km, the model shows that the maximum central density occurs for a maximal compactness value ρc = 7.8065214 × 1017kg/m3.

中文翻译：

---

表示致密恒星的单参数完美流体解

在描述中子星时，将引力理论视为广义相对论非常重要，因为对不同类型恒星的行为具有决定性影响，因为有些物体的密度甚至大于核密度。本文从完美流体的爱因斯坦方程开始，然后我们提出了一个单参数恒星模型，该模型允许用致密比描述中子星等致密物体你 ≤ 0.2533053. 压力和密度是单调递减的正则函数，声速满足因果关系，而其绝热指数的值γ = 4.9227102 > 4/3保证稳定性。此外，图磷相对ρ显示状态方程的准线性关系磷(ρ) = 磷C(ρ - ρb)/(ρC - ρb)，当我们有夸克之间的相互作用时，这类似于所谓的 MIT Bag 方程。在我们的例子中，这是由于在恒星内部发现的不同成分的相互作用，例如电子和中子。作为该模型的应用，我们描述了恒星 PSR J1614-2230，观测到的质量为米 = (1.97 ± 0.04)米⊙和一个半径R = (13 ± 2)公里, 该模型表明最大中心密度出现在最大紧实度值ρC = 7.8065214 × 1017公斤/米3.