An anisotropic interior solution of Einstein equations

Abstract

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.