  Neutron star (binary neutron star and neutron star - black hole) mergers are
believed to produce short-duration gamma-ray bursts. They are also believed to
be the dominant source of gravitational waves to be detected by the advanced
LIGO and the dominant source of the heavy r-process elements in the universe.
Whether or not these mergers produce short-duration GRBs depends sensitively on
the fate of the core of the remnant (whether, and how quickly, it forms a black
hole). In this paper, we combine the results of merger calculations and
equation of state studies to determine the fate of the cores of neutron star
mergers. Using population studies, we can determine the distribution of these
fates to compare to observations. We find that black hole cores form quickly
only for equations of state that predict maximum non-rotating neutron star
masses below 2.3-2.4 solar masses. If quick black hole formation is essential
in producing gamma-ray bursts, LIGO observed rates compared to GRB rates could
be used to constrain the equation of state for dense nuclear matter.
