The neutron star tidal deformability is a critical parameter which determines
the pre-merger gravitational-wave signal in a neutron star merger. In this
article, we show how neutron star tidal deformabilities behave in the presence
of one or two sharp phase transition(s). We characterize how the tidal
deformability changes when the properties of these phase transitions are
modified in dense matter equation of state (EoS). Sharp phase transitions lead
to the smallest possible tidal deformabilities and also induce discontinuities
in the relation between tidal deformability and gravitational mass. These
results are qualitatively unmodified by a modest softening of the phase
transition. Finally, we test two universal relations involving the tidal
deformability and show that their accuracy is limited by sharp phase
transitions.Comment: 20 pages, 18 figures; accepted for publication in PR
