Prospects for Direct Detection of Black Hole Formation in Neutron Star Mergers with Next-Generation Gravitational-Wave Detectors

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.