  We investigate the hadron-quark phase transition inside neutron stars and
obtain mass-radius relations for hybrid stars. The equation of state for the
quark phase using the standard NJL model is too soft leading to an unstable
star and suggesting a modification of the NJL model by introducing a momentum
cutoff dependent on the chemical potential. However, even in this approach, the
instability remains. In order to remedy the instability we suggest the
introduction of a vector coupling in the NJL model, which makes the EoS
stiffer, reducing the instability. We conclude that the possible existence of
quark matter inside the stars require high densities, leading to very compact
stars.
