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With the first detection of gravitational waves from a binary system of neutron
stars, GW170817, a new window was opened to study the properties of matter at
and above nuclear-saturation density. Reaching densities a few times that of
nuclear matter and temperatures up to 100 MeV, such mergers represent potential
sites for a phase transition from confined hadronic to deconfined quark matter.
While for GW170817 the postmerger signal could not be detected, such a signal
will be a powerful observable in the near future. In this seminar I will
present the possible scenarios of how a phase transition to quark-gluon plasma
can take place in the postmerger phase of a binary neutron star merger. I will
focus on the most recently explored scenario of a so-called ``delayed phase
transition'', where the merger remnant transitions from a purely hadronic
hypermassive neutron star to a meta-stable hypermassive hybrid star with a
dense quark core. This process promises to yield the strongest signature in the
gravitational-wave signal for the production of quark matter in the present