Hybrid Stars in the Framework of different NJL Models
  We compute models for the equation of state (EoS) of the matter in the cores of hybrid stars. Hadronic matter is treated in the non-linear relativistic mean-field approximation, and quark matter is modeled by three-flavor local and non-local Nambu$-$Jona-Lasinio (NJL) models with repulsive vector interactions. The transition from hadronic to quark matter is constructed by considering either a soft phase transition (Gibbs construction) or a sharp phase transition (Maxwell construction). We find that high-mass neutron stars with masses up to $2.1-2.4 M_\odot$ may contain a mixed phase with hadrons and quarks in their cores, if global charge conservation is imposed via the Gibbs conditions. However, if the Maxwell conditions is considered, the appearance of a pure quark matter core either destabilizes the star immediately (commonly for non-local NJL models) or leads to a very short hybrid star branch in the mass-radius relation (generally for local NJL models). 
G. A. Contrera, M. Orsaria, I. F. Ranea-Sandoval and F. Weber
nucl-th astro-ph.HE astro-ph.SR hep-ph