In this report, we present an interior solution to Einstein’s equations in a spherically symmetric and static spacetime filled by two sources with anisotropic pressures, one of these of ordinary matter for which the radial pressure is described by the MIT Bag state equation associated to the presence of quarks and the other by non-ordinary quintessence type matter. The solution is obtained from imposing the Karmarkar condition considering a metric function [Formula: see text] resulting in a physically acceptable, stable and adequate model to represent compact objects with compactness rate [Formula: see text]. Which allows to take different value of mass and radius in the range of the observational data of mass [Formula: see text] and radius [Formula: see text] of the star 4U1608-52 with compactness [Formula: see text], from these data we determine the range of [Formula: see text].

Starting from the known condition of Karmarkar, which guarantees that a static and spherically symmetrical space-time is embedded in a manifold of dimension 5, and that it generates a differential equation between the metric coefficients [Formula: see text] and [Formula: see text], we solve Einstein’s equations for a fluid with anisotropic pressures. This allows us to represent the interior of the neutron star EXO 1785-248, with observational data around the pair of mass and radius [Formula: see text], [Formula: see text] and [Formula: see text], [Formula: see text]. It is shown that the density, radial and tangential pressure are monotonically decreasing functions, while the radial and tangential speeds of sound satisfy the causality conditions. The model presented depends on the compactness [Formula: see text] and two other parameters that characterize the internal behavior of the Hydrostatic variables, in particular the values of the central density [Formula: see text]. In particular for the observational values of mass and radius [Formula: see text], we have [Formula: see text] meanwhile that for [Formula: see text] we have [Formula: see text]. In a complementary manner it is shown that the model satisfies the causality condition and that according to the stability criteria of Harrison–Zeldovich–Novikov and of cracking the solution is stable.

In this work, the analysis of the behavior of an interior solution in the frame of Einstein’s general theory of relativity is reported. Given the possibility that, for greater densities than the nuclear density, the matter presents anisotropies in the pressures and that these are the orders of density present in the interior of the compact stars, the solution that is discussed considers that the interior region contains an anisotropic fluid, i.e. [Formula: see text]. The compactness value, where [Formula: see text], for which the solution is physically acceptable is [Formula: see text] as such the graphic analysis of the model is developed for the case in which the mass [Formula: see text] and the radius [Formula: see text] which corresponds to the star Her X-1, with maximum compactness [Formula: see text], although for other values of compactness [Formula: see text] the behavior is similar. The functions of density and pressures are positive, finite and monotonically decreasing, also the solution is stable according to the cracking criteria and the range of values is consistent with what is expected for these type of stars.