In order to study the gravitational collapse of charged matter we analyze the simple model of an self-gravitating massless scalar field coupled to the electromagnetic field in spherical symmetry. The evolution equations for the Maxwell–Klein–Gordon sector are derived in the 3+1\documentclass[12pt]{minimal}
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\begin{document}$$3+1$$\end{document} formalism, and coupled to gravity by means of the stress–energy tensor of these fields. To solve consistently the full system we employ a generalized Baumgarte–Shapiro–Shibata–Nakamura formulation of General Relativity that is adapted to spherical symmetry. We consider two sets of initial data that represent a time symmetric spherical thick shell of charged scalar field, and differ by the fact that one set has zero global electrical charge while the other has non-zero global charge. For compact enough initial shells we find that the configuration doesn’t disperse and approaches a final state corresponding to a sub-extremal Reissner–Nördstrom black hole with |Q|<M\documentclass[12pt]{minimal}
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\begin{document}$$|Q|<M$$\end{document}. By increasing the fundamental charge of the scalar field q\documentclass[12pt]{minimal}
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\begin{document}$$q$$\end{document} we find that the final black hole tends to become more and more neutral. Our results support the cosmic censorship conjecture for the case of charged matter.
