  We study the lifetimes of the remnant produced by the merger of two neutron
stars and revisit the determination of the threshold mass to prompt collapse,
$M_{\rm th}$. Using a fully general-relativistic numerical approach and a novel
method for a rigorous determination of $M_{\rm th}$, we show that a nonlinear
universal relation exists between the threshold mass and the maximum
compactness. For the temperature-dependent equations of state considered here,
our results improve a similar linear relation found recently with methods that
are less accurate but yield quantitatively similar results. Furthermore,
exploiting the information from GW170817, we use the universal relation to set
lower limits on the stellar radii for any mass.
