Fundamental-mode eigenfrequencies of neutral and charged twin neutron stars

We investigate the effects of rapid and slow conversions on the fundamental-mode eigenfrequencies of hybrid neutron stars having highly discontinuous transitions between hadronic and quark matter, the so-called twin stars. We analyze some characteristic cases in the available parameter space of the equations of state for the hadronic and quark phases. Furthermore, we also consider the possibility that these stellar configurations are electrically charged. Our results indicate that for neutral configurations under rapid conversions the stability window coincides with the usual stability criterion, i.e. $\partial$M/$\partial$p${}_c$ > 0 and that the two branches are disconnected. This discontinuity remains when electric charge is considered, but the usual criterion is not sufficient to determine the star's stability. On the other hand, slow conversions connect initially disconnected branches and increase the stability window of the hybrid configurations. For both conversion speeds, the presence of electric charge diminishes the magnitude of the eigenfrequencies and its stability window.