Cosmic censorship in higher dimensions

We show that the naked singularities arising in dust collapse from smooth initial data (which include those discovered by Eardley and Smarr, Christodoulou, and Newman) are removed when we make a transition to higher dimensional spacetimes. Cosmic censorship is then restored for dust collapse, which will always produce a black hole as the collapse end state for dimensions D⩾6, under conditions to be motivated physically such as the smoothness of initial data from which the collapse develops.