The relevance of anisotropy in compact models is shown by the construction of a stellar model, this can influence the behavior of density, pressure and speed of sound in such grade that if the anisotropy disappear it could produce a regular model of perfect fluid which is not physically acceptable. The present anisotropic model has dependence in two parameters n associated with the anisotropy and w related with the rate of compactness u = G M/c 2 R, this is regular and physically acceptable. That is the speed of sound is positive and lower than the light speed, the density as well as radial and tangential pressure are monotonic decrescent functions. The compactness values for which the radial and tangential speed of sound are monotonic decrescent functions and the solution is potentially stable occurs for u ≤ 0.2073450586, and in particular for the maximum value of u n ∈ [−0.771108398, −0.231572621]. While if n = 1 we get a model of perfect regular fluid but the density and speed of sound can not be both positive at the origin, so the solution is not physically acceptable in the absence of anisotropic pressures.

An analysis and construction is presented for a stellar model characterized by two parameters (w, n) associated with the compactness ratio and anisotropy, respectively. The reliability range for the parameter w [Formula: see text] 1.97981225149 corresponds with a compactness ratio u [Formula: see text] 0.2644959374, the density and pressures are positive, regular and monotonic decrescent functions, the radial and tangential speed of sound are lower than the light speed, moreover, than the plausible stability. The behavior of the speeds of sound are determinate for the anisotropy parameter n, admitting a subinterval where the speeds are monotonic crescent functions and other where we have monotonic decrescent functions for the same speeds, both cases describing a compact object that is also potentially stable. In the bigger value for the observational mass M = 2.05 M[Formula: see text] and radii R = 12.957 Km for the star PSR J0348+0432, the model indicates that the maximum central density [Formula: see text] = 1.283820319 × 10[Formula: see text] Kg/m3 corresponds to the maximum value of the anisotropy parameter and the radial and tangential speed of the sound are monotonic decrescent functions.

In this paper, we present a physically acceptable internal solution with a perfect fluid, which needs the pressure and density as regular, positive and monotonic decreasing functions and with a speed of sound positive and lower than the speed of light. This solution depends on a parameter [Formula: see text], and it is physically acceptable if [Formula: see text], the compactness has a maximum value for the maximum value of [Formula: see text] and it corresponds to [Formula: see text], thus the model can be applicable to the description of compact stars. In a complementary way, we present the description of a star with mass equal to the sun mass and radius of [Formula: see text] Km associated to the neutron star Her X-1, obtaining a central density [Formula: see text] which is characteristic of the neutron stars.

A relativistic, static and spherically symmetrical stellar model is presented, constituted by a perfect charged fluid. This represents a generalization to the case of a perfect neutral fluid, whose construction is made through the solution to the Einstein-Maxwell equations proposing a form of gravitational potential  $g_{tt}$ and the electric field. The choice of electric field implies that this model supports values of compactness$u=GM/c^2R\leq 0.5337972212$, values higher than the case without electric charge ($u\leq 0.3581350065$), being this feature of relevance to get to represent compact stars. In addition, density and pressure are positive functions, bounded and decreasing monotones, the electric field is a monotonously increasing function as well as satisfying the condition of causality so the model is physically acceptable. In a complementary way, the internal behavior of the hydrostatic functions and their values are obtained taking as a data the corresponding to a star of $1 M_\odot$,for different values of the charge parameter, obtaining an interval for the central density $\rho_c\approx (7.9545,2.7279) 10^{19}$ $ Kg/m^3$ characteristic of compact stars.

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