  Inspiraling and merging binary neutron stars (BNSs) are important sources of
both gravitational waves and coincident electromagnetic counterparts. If the
BNS total mass is larger than a threshold value, a black hole ensues promptly
after merger. Through a statistical study in conjunction with recent LIGO/Virgo
constraints on the nuclear equation of state, we estimate that up to $\sim
25\%$ of BNS mergers may result in prompt collapse. Moreover, we find that most
models of the BNS mass function we study here predict that the majority of
prompt-collapse BNS mergers have $q\gtrsim 0.8$. Prompt-collapse BNS mergers
with mass ratio $q \gtrsim 0.8$ may not be accompanied by detectable kilonovae
or short gamma-ray bursts, because they unbind a negligible amount of mass and
form negligibly small accretion disks onto the remnant black hole. We call such
BNS mergers "orphan". However, recent studies have found that
${10^{41-43}(B_p/10^{12}\rm G)^2 erg\, s^{-1}}$ electromagnetic signals can be
powered by magnetospheric interactions several milliseconds prior to merger.
Moreover, the energy stored in the magnetosphere of an orphan BNS merger
remnant will be radiated away in ${\mathcal O}(1\ \rm ms)$. Through simulations
in full general relativity of BNSs endowed with an initial dipole
magnetosphere, we find that the energy in the magnetosphere following black
hole formation is $E_B \sim 10^{39-41} (B_p/10^{12}\rm G)^2$ erg. Radiating
$\sim 1\%$ of $E_B$ in 1 ms, as has been found in previous studies, matches the
premerger magnetospheric luminosity. These magnetospheric signals are not
beamed, and their duration and power agrees with those of non-repeating fast
radio bursts (FRBs). These results combined with our statistical study suggest
that a non-repeating FRB may be the most likely electromagnetic counterpart of
prompt-collapse BNSs.
