We propose the study of the cooling and of the hydrodynamic rearrangement of neutrons stars after the transition to quark matter inside star's core. Among the motivations to this study, we have the possible association between neutron stars and short-duration gamma-ray bursts (GRBs). As a first stage, we aim the study of the star's cooling due to the diffusive emission of the neutrinos generated in the central quark core. In our model, in which we assume spherical symmetry, constant number of baryons and a diffusive regime; the computational method to be applied resembles that of the pioneer work of Burrows & Lattimer, with the appropriate diffusion coefficients. In a second moment, we turn our attention to the neutron star's hydrodynamics, with the objective of tracking its evolution during the first seconds following the arise of the quark core. At this time we will be able to investigate eventual shock and gravitational waves and the possibility of matter ejection by the star. With this, we intend to acquire a wide range of theoretical understanding from both neutrino cooling and hydrodynamic point of views about neutron stars that come to develop a quark core.
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