UNDERSTANDING CRITICAL COLLAPSE OF A SCALAR FIELD

I construct a spherically symmetric solution for a massless real scala r field minimally coupled to general relativity which is discretely se lf-similar (DSS) and regular. This solution coincides with the interme diate attractor found by Choptuik in critical gravitational collapse. The echoing period is Delta = 3.4453 +/- 0.0005. The solution is conti nued to the future self-similarity horizon, which is also the future l ight cone of a naked singularity. The scalar field and metric are C-1 but not C-2 at this Cauchy horizon. The curvature is finite neverthele ss, and the horizon carries regular null data. These are very nearly f lat. The solution has exactly one growing perturbation mode, thus conf irming the standard explanation for universality. The growth of this m ode corresponds to a critical exponent of gamma = 0.374 +/- 0.001, in agreement with the best experimental value. I predict that in critical collapse dominated by a DSS critical solution, the scaling of the bla ck hole mass shows a periodic wiggle, which like gamma is universal. M y results carry over to the free complex scalar field. Connections wit h previous investigations of self-similar scalar field solutions are d iscussed, as well as an interpretation of Delta and gamma as anomalous dimensions.