Charge scaling and universality in critical collapse

Consider any one-parameter family of initial data such that data with a 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 similar to(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+\(partial derivative+iqA)phi\(2)+F-2, we consider initial data with spherical symmetry and a 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 similar to(p-p*)(gamma), and the black hole charge as Q similar to(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 greater than or equal to 2 gamma. We suggest the existence of universality classes with respect to parameters such as q.