Non-Radial Neutrino Emission upon Black Hole Formation in Core Collapse Supernovae

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.