Abstract
A new interior solution of Einstein’s equations is derived for a static and spherically symmetric space–time that contains fluid with anisotropic pressures, characterized by a parameter N. The model presented is a generalization to a proposal which contemplated a perfect fluid, which allows us to do an analysis of the impact of the anisotropy on the compactness, density and speed of sound. Taking the observational data of the mass M=1.7M⊙ and radius R=9 km as well as the mass M=1.4M⊙ and radius R=11km reported for the star EXO 1745-248, it is determined that the range of values of the density varies between 5.7651×1017 and 1.0937×1018 and these increase as the anisotropy parameter increases; it also shows an effect of the anisotropy on the speed of sound. The stability of the solution is shown through the Zeldovich criteria and through the adiabatic index, and from a graphic analysis it is verified that the behavior of the density, pressures and speed of sound are physically acceptable.
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