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A charged stellar model is presented by constructing a solution to the Einstein–Maxwell equations system in a spherically symmetrical static time-space. The rate of compactness for the model depends on two parameters [Formula: see text], one of them [Formula: see text] associated to the charge, which allows a value of compactness [Formula: see text] higher than the neutral case. The density and pressure are regular functions, positive and monotonically decreasing and the function of charge is positive regular and monotonically increasing, its shown that the model satisfies the condition of causality, the geometry is regular and as such the model is physically acceptable. Although the model can be applicable for a variety of stars, considering a star with mass [Formula: see text] for [Formula: see text] the range of compactness is [Formula: see text] and radius [Formula: see text], in this case the range of values for the central density is [Formula: see text] greater than the value of the nuclear density and consistent with that expected for stars with this compactness rate.

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A compact star model formed by quintessence and ordinary matter is presented, both sources have anisotropic pressures and are described by linear state equations, also the state equation of the tangential pressure for the ordinary matter incorporates the effect of This is an Open Access article published by World Scientific Publishing Company. It is distributed under the terms of the Creative Commons Attribution 4.0 (CC BY) License which permits use, distribution and reproduction in any medium, provided the original work is properly cited.* Corresponding author. 2050144-1 Mod. Phys. Lett. A 2020.35. Downloaded from www.worldscientific.com by 44.224.250.200 on 07/11/20. Re-use and distribution is strictly not permitted, except for Open Access articles. G. Estevez-Delgado et al.the quintessence. It is shown that depending on the compactness of the star u = GM/c 2 R the constant of proportionality µ between the density of the ordinary matter and the radial pressure, Pr = µc 2 (ρ − ρ b ), has an interval of values which is consistent with the possibility that the matter is formed by a mixture of particles like quarks, neutrons and electrons and not only by one type of them. The geometry is described by the Durgapal metric for n = 5 and each one of the pressures and densities is positive, finite and monotonic decreasing, as well as satisfying the condition of causality and of stability v 2 t − v 2 r < 0, which makes our model physically acceptable. The maximum compactness that we have is u ≤ 0.28551, so we can apply our solution considering the observational data of mass and radii M = (2.01 ± 0.04) M ⊙ , R ∈ [12.062, 12.957] km which generate a compactness 0.22448 ≤ u ≤ 0.25448 associated to the star PSR J0348 + 0432. In this case, the interval of µ ∈ [0.78055, 1] and its maximum central density ρc and in the surface ρ b of the star are ρc = 7.0387 × 10 17 kg/m 3 and ρ b = 4.6807 × 10 17 kg/m 3 , respectively, meanwhile the central density of the quintessence ρqc = 3.4792 × 10 16 kg/m 3 .

A stellar model with anisotropic pressure is constructed and analyzed, the metric components that describe the geometry and the source of matter satisfy Einstein’s equations and both are finite inside the star. In addition, density and pressure are decreasing monotone functions of the radial distance. The speed of sound is positive and less than the speed of light, furthermore the model is potentially stable. The model allows describing compact objects with compactness of [Formula: see text] and as a result of the anisotropic value there is a range of values of the central density, in particular for the maximum value of compactness a star with [Formula: see text] and a value of anisotropic parameter [Formula: see text] we get a stellar radius of [Formula: see text] and a central density [Formula: see text]. The above makes the solution a physically realistic model that can be used to describe dense objects such as neutron stars whose characteristic density is of the order of nuclear density.