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The investigation of the phase state of dense matter is hindered bycomplications of first-principle nonperturbative quantum chromodynamics. Byperforming the first consistent general-relativistic calculations oftidal-excited g-mode of neutron stars with a first-order strong interactionphase transition in the high-density core, we demonstrate that gravitationalwave signal during binary neutron star inspiral probes their innermosthadron-quark transition and provides potent constraints from present and futuregravitational-wave detectors.

Resolving phase transition properties of dense matter through tidal-excited g-mode from inspiralling neutron stars