  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
Witten's $strange$ $matter$ 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.
