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 equalmass 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.

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