Scalar field collapse and cosmic censorship

We analyze here the final fate of complete gravitational collapse of a massless scalar field within general relativity. A class of dynamical solutions with initial data close to the Friedmann-Lemaitre-Robertson-Walker (FLRW) collapse model is explicitly given and the Einstein equations are integrated numerically in a neighborhood of the center. We show that the initial data space is evenly divided between the dynamical evolutions that terminate in a black hole final state and those that produce a locally naked singularity. We comment on the genericity aspects of the collapse end-states and the connection to cosmic censorship conjecture is pointed out.