Critical behavior and universality in gravitational collapse of a charged scalar field

We summarize results from a study of spherically symmetric collapse of a charged (complex) massless scalar field. We present an analytic argument which conjectures the generalization of the mass-scaling relation and echoing phenomena, originally discovered by Choptuik, for the charged case. Furthermore, we study the behavior of the self-similar critical solution under external perturbations — addition of a cosmological constant $\Lambda$ and under a variation of the charge coupling constant $e$. Finally, we study the scaling relation of the black-hole charge. Using an analytic argument, we conjecture that black holes of infinitesimal mass are neutral or obey the relation $Q_{\mathrm{BH}}\ll M_{\mathrm{BH}}.$ We verify our predictions with numerical results.