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This thesis work focuses on studying the possible existence of phasetransitions in the immediate compact remnants of core collapse supernova,neutron stars, and the theoretical models that describe the interior of densematter. Specifically, we are interested in analyzing the feasibility of atransition from hadronic matter to quark matter in the cores of these objects.For the phase transition we will use two different formalisms: the Maxwellformalism or abrupt phase transition and the Gibbs formalisms or mixed phasetransition. For the description of hadronic matter, we will use differentparametrizations of the relativistic mean field model with density-dependentcoupling constants. For the description of quark matter we will use aneffective nonlocal Nambu Jona-Lasinio model of three flavors with vectorinteractions, in which we will include the possibility of formation of diquarksto model a superconducting phase of color in $SU(3)$. Phase diagrams andequations of state of quark matter at finite temperature are presented, and theinfluence of that type of matter on observables associated with neutron starsis investigated. The simplified thermal evolution of compact stars during theirformation is studied, from their state of proto-neutron stars to that of coldneutron stars, and the results obtained are compared with recent astrophysicalobservations. The results obtained indicate that the occurrence of quark matterin the nuclei of these stars remains a promising possibility. The fact that theuse of more realistic models for the description of the dense matter in theseobjects indicates the presence of quark matter inside neutron stars, could bean answer to the question of the behavior of that kind of matter and thedetermination of its corresponding equation of state.

Non-local quark models for description of dense matter in the cores of neutron stars