  A direct detection of black hole formation in neutron star mergers would
provide invaluable information about matter in neutron star cores and finite
temperature effects on the nuclear equation of state. We study black hole
formation in neutron star mergers using a set of 190 numerical relativity
simulations consisting of long-lived and black-hole-forming remnants. The
postmerger gravitational-wave spectrum of a long-lived remnant has greatly
reduced power at a frequency $f$ greater than $f_{\rm peak}$, for $f \gtrsim
4\,\rm kHz$, with $f_{\rm peak} \in [2.5, 4]\,\rm kHz$. On the other hand,
black-hole-forming remnants exhibit excess power in the same large $f$ region
and manifest exponential damping in the time domain characteristic of a
quasinormal mode. We demonstrate that the gravitational-wave signal from a
collapsed remnant is indeed a quasinormal ringing. We report on the opportunity
for direct detections of black hole formation with next-generation
gravitational-wave detectors such as Cosmic Explorer and Einstein Telescope and
set forth the tantalizing prospect of such observations up to a distance of 100
Mpc for an optimally oriented and located source with an SNR of 4.
