  Mergers of neutron stars with black holes have been suggested as candidates
for short gamma-ray bursts. They have also been studied for their potential as
gravitational wave sources observable with ground-based detectors. For these
purposes, it is important to know under what circumstances such a merger could
leave an accretion disk or result in a period of stable mass transfer. We show
that, consistent with recent numerical simulations, it is expected that mergers
between neutron stars and black holes will be prompt, with no accretion disk
and no stable mass transfer, if the black hole has a mass greater than that of
the neutron star and is spinning slowly. The reason is that for comparable
masses, angular momentum loss to gravitational radiation starts a plunge orbit
well outside the innermost stable circular orbit, causing direct merging rather
than extended mass transfer. Even when the black hole is spinning rapidly and
exactly prograde with respect to the orbit, we show that it is possible within
current understanding that no accretion disk will form under any circumstances,
but resolution of this will require full general relativistic numerical
simulations with no approximations.
