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The cold quark matter with high chemical potential can exist in nature only inside the neutron stars. In this talk we will present some results of the study of hybrid state equations of cold quark matter in this type of star, from hadron $\rightarrow$ quarks phase transitions using Maxwell’s construction.

The main goal of this work is the study of cold quark matter in neutron stars from phase transitions of hadronic matter to quark matter. In this work, after presenting important aspects of stellar evolution and the theory of neutron stars, we review two frameworks designed to calculate the structure of the stars in the relativistic regime: the canonical Tolman-Oppenheimer-Volkoff equations and the so called ‘new paradigm’ Einstein-Maxwell-Fermi, where we conclude that the Einstein-Maxwell-Fermi model has some inconsistencies, being inadequate for the treatment of stars with hybrid equation of state, and the fact that using the atomic model as a starting point already has the property of the local non-neutrality as a built-in feature.

Every programmer probably had some training in learning a language or framework – but how did you learn to fix the defects in your software? When you fell in love with programming (or at least decided it was a remunerative career), you probably thought of it as a creative endeavor.

Recently, it has been suggested that a critical electrical field arises during the gravitational collapse of massive stars leading to a vacuum polarization. This, in turn, leads to the necessity of a reexamination of the gravito-electrodynamical properties of compact stars of the class of neutron stars.

From the moment software products are delivered, they go through a series of modifications during their life-cycle. The maintenance process can either be corrective or evolutionary/adaptive. A corrective process is used to fix implementation errors and an evolutionary/adaptive process is used to improve performance and structure or other attributes, or to adapt the product to a changed environment, according to requests from users.