  We consider here the classic scenario given by Oppenheimer, Snyder, and Datt,
for the gravitational collapse of a massive matter cloud, and examine its
stability under the introduction of small tangential stresses. We show, by
offering an explicit class of physically valid tangential stress perturbations,
that an introduction of tangential pressure, however small, can qualitatively
change the final fate of collapse from a black hole final state to a naked
singularity. This shows instability of black hole formation in collapse and
sheds important light on the nature of cosmic censorship hypothesis and its
possible formulations. The key effect of these perturbations is to alter the
trapped surface formation pattern within the collapsing cloud and the apparent
horizon structure. This allows the singularity to be visible, and implications
are discussed.
