Abstract
In this paper, we generalize a method introduced by Christodoulou for studying the Einstein-scalar field to prove a trapped surface formation criterion for the Einstein–Maxwell-charged scalar field system under spherical symmetry. If we further require the initial charge to be sufficiently small, we obtain an almost-scale-critical result in the perturbative regime. In the “Appendix”, we also include a proof of Christodoulou’s result on trapped surface formation for the Einstein-scalar field using double null coordinates, as well as a strengthed scale-critical criterion in the case of Minkowskian incoming characteristic initial data.
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