  Black hole formation in a core-collapse supernova is expected to lead to a
distinctive, abrupt drop in neutrino luminosity due to the engulfment of the
main neutrino-producing regions as well as the strong gravitational redshift of
those remaining neutrinos which do escape. Previous analyses of the shape of
the cut-off have focused on specific trajectories or simplified models of bulk
neutrino transport. In this article, we integrate over simple "ballistic"
geodesics to investigate potential effects on the cut-off profile of including
all neutrino emission angles from a collapsing surface in the Schwarzschild
metric, and from a contracting equatorial mass ring in the Kerr metric. We find
that the non-radial geodesics contribute to a softening of the cut-off in both
cases. In addition, extreme rotation introduces significant changes to the
shape of the tail which may be observable in future neutrino detectors, or
combinations of detectors.
