Short range correlations are introduced using unitary correlation method in a relativistic approach to the equation of state of the infinite nuclear matter in the framework of the Hartree-Fock approximation. The effect of the correlations in the ground state properties of the nuclear matter is studied.

In order to investigate the instabilities in asymmetric nuclear matter described within relativistic mean field hadron models, we build the spinodals. We have used relativistic models both with constant and density dependent couplings at zero and finite temperatures. We have seen that the main differences in the spinodals occur at finite temperature and large isospin asymmetry close to the boundary of the instability regions.

We investigate the properties of mixed stars formed by hadronic and quark matter in beta-equilibrium described by appropriate equations of state (EOS) in the framework of relativistic mean-field theory. We use the non-linear Walecka model for the hadron matter and the MIT Bag and the Nambu-Jona-Lasinio models for the quark matter. The calculations were performed for T = 0 and for finite temperatures in order to describe neutron and proto-neutron stars. The star properties are discussed. Both the Bag model and the NJL model predict a mixed phase in the interior of the star.