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The search for the true ground state of the dense matter remains open sinceBodmer, Terazawa and other raised the possibility of stable quarks, boosted byWitten's $strange$ $matter$ hypothesis in 1984. Within this proposal, thestrange matter is assumed to be composed of $strange$ quarks in addition to theusual $up$s and $down$s, having an energy per baryon lower than the strangelesscounterpart, and even lower than that of nuclear matter. In this sense, neutronstars should actually be strange stars. Later work showed that a paired,symmetric in flavor, color-flavor locked (CFL) state would be preferred to theone 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 veryaccurate, CFL equation of state (EoS) that generalizes the MIT bag model toobtain two families of exact solutions for the static Einstein field equationsconstructing families anisotropic compact relativistic objects. In thisfashion, we provide exact useful solutions directly connected withmicrophysics.

Exact solutions for compact stars with CFL quark matter