  Consider any 1-parameter family of initial data such that data with parameter
value p > p* form black holes, and data with p < p* do not. As p -> p* from
above ("critical collapse"), the black hole mass scales as M ~ (p-p*)^gamma,
where the critical exponent gamma is the same for all such families of initial
data. So far critical collapse has been investigated only for initial data with
zero charge and zero angular momentum. Here we allow for U(1) charge. In scalar
electrodynamics coupled to gravity, with action R + |(d + iqA) phi|^2 + F^2, we
consider initial data with spherical symmetry and nonvanishing charge. From
dimensional analysis and a previous calculation of Lyapunov exponents, we
predict that in critical collapse the black hole mass scales as M ~
(p-p*)^gamma, and the black hole charge as Q ~ (p-p*)^delta, with gamma = 0.374
+- 0.001 (as for the real scalar field), and delta = 0.883 +- 0.007. We
conjecture that, where there is no mass gap, this behavior generalizes to other
charged matter models, with delta \ge 2 gamma. We suggest the existence of
universality classes with respect to parameters such as q.
