We investigate some models of compact objects in the general relativity theory with cosmological constant Λ, based on two density profiles, one of them attributed to Stewart and the other one to Durgapal and Bannerji, proposed in the literature to model “neutron stars”. For them, a nonlocal equation of state with cosmological constant is obtained as a consequence of the chosen metric. In another direction, we obtain a solution for configurations with null radial pressure. The first model (based on Stewart’s density profile) turned out to be the most interesting, since surprisingly it admits the presence of dark energy in the interior of the star, in the outermost layers, for a certain range of mass–radius ratio γ. This dark energy is independent of the cosmological constant, since it is a consequence of the tangential pressure of the fluid be sufficiently negative. Still in this case, for other values of γ, all the energy conditions are satisfied. Another advantage of this model, as well as that based on the density profile of Durgapal and Bannerji, is the existence of intervals of γ compatible with physically acceptable models for Λ < 0, Λ = 0 and Λ > 0, which also allowed us to analyze the influence of Λ on the behavior of the fluid with respect to the energy conditions. The other configuration studied here, Pr = 0, only allows solutions for Λ < 0, in order to ensure a positive mass for the object and to satisfy all the energy conditions in a specific range of γ.

中文翻译：

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带有局部暗能量壳的致密物体

我们研究了广义相对论中具有宇宙常数的致密物体的一些模型Λ，基于两个密度分布，其中一个归因于斯图尔特，另一个归因于 Durgapal 和 Bannerji，在文献中提出来模拟“中子星”。对他们来说，作为所选度量的结果，获得了具有宇宙学常数的非局部状态方程。在另一个方向上，我们获得了径向压力为零的配置的解决方案。第一个模型（基于斯图尔特的密度分布）被证明是最有趣的，因为令人惊讶的是，它承认在一定质量半径比范围内，恒星内部、最外层存在暗能量γ. 这种暗能量与宇宙常数无关，因为它是流体切向压力足够负的结果。仍然在这种情况下，对于其他值γ，满足所有能量条件。该模型以及基于 Durgapal 和 Bannerji 密度分布的模型的另一个优点是存在γ与物理上可接受的模型兼容Λ < 0,Λ = 0和Λ > 0，这也使我们能够分析Λ关于流体相对于能量条件的行为。这里研究的另一种配置，磷r = 0，只允许解决方案Λ < 0，以确保物体的正质量并满足特定范围内的所有能量条件γ.