  Using hydrodynamical simulations for a large set of high-density matter
equations of state (EoSs) we systematically determine the threshold mass
M_thres for prompt black-hole formation in equal-mass and asymmetric neutron
star (NS) mergers. We devise the so far most direct, general and accurate
method to determine the unknown maximum mass of nonrotating NSs from merger
observations revealing M_thres. Considering hybrid EoSs with hadron-quark phase
transition, we identify a new, observable signature of quark matter in NS
mergers. Furthermore, our findings have direct applications in gravitational
wave searches, kilonova interpretations and multi-messenger constraints on NS
properties.
