Hadron-quark phase transition: the QCD phase diagram and stellar conversion

Different extensions of the Nambu-Jona-Lasinio model, known to satisfy expected QCD chiral symmetry aspects, are used to investigate a possible hadron-quark phase transition at zero temperature and to build the corresponding binodal sections. We have shown that the transition point is very parameter dependent and that both pressure and chemical potential increase drastically with the increase of the vector interaction strength in the quark sector. $\beta$-equilibrium and charge neutrality are also incorporated to the models so that the investigation can be extrapolated to stellar matter. In this case, two different scenarios are analyzed, both constrained to the fact that the conversion is restricted to a situation where there is no strangeness in the hadronic star matter, but it is incorporated in the quark star matter. The same conclusions drawn before with respect to the coexistence pressure and chemical potentials are reinforced, but we have checked that even if a transition from a metastable hadronic star to a quark star is thermodynamically possible, it is either energetically forbidden or gives rise to a black hole. It is shown that the vector interaction can be strong enough to inhibit the softening of the equation of state when the $s$-quark sets in.