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 .