  The collapse of a massive star with low angular momentum content is commonly
argued to result in the formation of a black hole without an accompanying
bright transient. Our goal in this Letter is to understand the flow in and
around a newly-formed black hole, involving accretion and rotation, via general
relativistic hydrodynamics simulations aimed at studying the conditions under
which infalling material can accrete without forming a centrifugally supported
structure and, as a result, generate no effective feedback. If the feedback
from the black hole is, on the other hand, significant, the collapse would be
halted and we suggest that the event is likely to be followed by a bright
transient. We find that feedback is only efficient if the specific angular
momentum of the infalling material at the innermost stable circular orbit
exceeds that of geodesic circular flow at that radius by at least $\approx
20\%$. We use the results of our simulations to constrain the maximal stellar
rotation rates of the disappearing massive progenitors PHL293B-LBV and
N6946-BH1, and to provide an estimate of the overall rate of disappearing
massive stars. We find that about a few percent of single O-type stars with
measured rotational velocities are expected to spin below the critical value
before collapse and are thus predicted to vanish without a trace.
