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Within the Lemaitre-Tolman-Bondi formalism for gravitational collapse ofinhomogeneous dust we analyze the parameter space that leads to the formationof a globally covered singularity (i.e. a black hole) when some physicallyreasonable requirements are imposed (namely positive radially decreasing andquadratic profile for the energy density and avoidance of shell crossingsingularities). It turns out that a black hole can occur as the endstate ofcollapse only if the singularity is simultaneous as in the standardOppenheimer-Snyder scenario. Given a fixed density profile then there is onevelocity profile for the infalling particles that will produce a black hole.All other allowed velocity profiles will terminate the collapse in a locallynaked singularity.

All black holes in Lemaitre-Tolman-Bondi inhomogeneous dust collapse