  Accurate modeling of the multi-messenger signatures connected to binary
neutron star mergers requires proper knowledge on the final remnant's fate and
the conditions under which black holes (BHs) can form in such mergers. In this
article, we use a suite of 84 numerical-relativity simulations in 28 different
physical setups to explore the impact of the individual stars' spin on the
merger outcome and on the early postmerger dynamics. We find that for setups
close to the prompt-collapse threshold, the stars' intrinsic spin significantly
changes the lifespan of the remnant before collapse and that the mass of the
debris disk surrounding the BH is also altered. To enable a better
understanding of BH formation, we check if there is at least a theoretical
chance of observing densities that are above the maximum density allowed in a
stable isolated neutron star, and we investigate the importance of different
pressure contributions on the evolution of the postmerger remnant and BH
formation.
