The search for the true ground state of the dense matter remains open since Bodmer, Terazawa and other raised the possibility of stable quarks, boosted by Wittens $strange$ $matter$ hypothesis in 1984. Within this proposal, the strange matter is assumed to be composed of $strange$ quarks in addition to the usual $up$s and $down$s, having an energy per baryon lower than the strangeless counterpart, and even lower than that of nuclear matter. In this sense, neutron stars should actually be strange stars. Later work showed that a paired, symmetric in flavor, color-flavor locked (CFL) state would be preferred to the one without any pairing for a wide range of the parameters (gap $Delta$, strange quark mass $m_s$, and bag constant B). We use an approximate, yet very accurate, CFL equation of state (EoS) that generalizes the MIT bag model to obtain two families of exact solutions for the static Einstein field equations constructing families anisotropic compact relativistic objects. In this fashion, we provide exact useful solutions directly connected with microphysics.
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