Cosmic censorship in higher dimensions. II.

Generalizing earlier results on dust collapse in higher dimensions, we show here that cosmic censorship can be restored in some classes of gravitational collapse models with tangential pressure present, if we take the spacetime dimension to be N≥6. This is under conditions to be motivated physically, such as smoothness of initial data from which the collapse develops. The models considered here with nonzero pressure include the Einstein cluster spacetimes which have been earlier studied extensively. Our work provides a step towards an understanding of the cosmic censorship conjecture and the necessary conditions for its validity.