The speculation discussed above that there may be no naked singularities formed for any regular initial data is in part based on the fact that the naked singularities that occur in scalar field collapse appear to be associated with the existence of type II critical collapse, while Vlasov matter is of type I. The primary goal in  was indeed to decide whether Vlasov matter is type I or type II.
These different types of matter are defined as follows. Given small initial data, no black holes form and matter will disperse. For large data, black holes will form and consequently there is a transition regime separating dispersion of matter and formation of black holes. If we introduce a parameter on the initial data such that for small dispersion occurs and for large a black hole is formed, we get a critical value separating these regions. If we take and denote by the mass of the black hole, then if as we have type II matter, whereas for type I matter this limit is positive and there is a mass gap. For more information on critical collapse we refer to the review paper by Gundlach .
The conclusion of  is that Vlasov matter is of type I. There are two other independent numerical simulations on critical collapse for Vlasov matter [128, 21]. In these simulations, maximal-areal coordinates are used rather than Schwarzschild coordinates as in . The conclusion of these studies agrees with the one in .
Living Rev. Relativity 14, (2011), 4
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