  Within the Lemaitre-Tolman-Bondi formalism for gravitational collapse of
inhomogeneous dust we analyze the parameter space that leads to the formation
of a globally covered singularity (i.e. a black hole) when some physically
reasonable requirements are imposed (namely positive radially decreasing and
quadratic profile for the energy density and avoidance of shell crossing
singularities). It turns out that a black hole can occur as the endstate of
collapse only if the singularity is simultaneous as in the standard
Oppenheimer-Snyder scenario. Given a fixed density profile then there is one
velocity profile for the infalling particles that will produce a black hole.
All other allowed velocity profiles will terminate the collapse in a locally
naked singularity.
