all families) having a value of about 0.37. The near critical evolution can be described by a universal solution of the field equations which also has a periodicity property called echoing, or discrete self-similarity. That is, it remains unchanged under a rescaling $(r,t)\rightarrow (e^{-n\Delta}r, e^{-n\Delta}t)$ of spacetime coordinates. $n$ is an integer, and $\Delta$ is about 3.4. Subsequently, these results have been confirmed by others.

At the critical solution, the mass of the forming black hole goes to zero, as $p\rightarrow p_{*}$ from the right. This critical solution is a naked singularity. However, since the naked singularity is realised for a specific solution in the one parameter family, it is a subset of measure zero. As regards cosmic censorship, the more significant feature are the black holes of arbitrarily small mass, and hence arbitrarily high curvature that is visible to a far away observer. It is more physical to think of censorship in terms of whether or not regions of unbounded high curvature are generically visible, and not just whether singularities are visible. Looked at in this way, scalar collapse provides a serious counterexample to censorship.

Similar critical behaviour has also been found in numerical studies of collapse with other 