The global structure of spherically symmetric charged scalar field spacetimes

Abstract: We initiate the mathematical study of spherical collapse of self-gravitating charged scalar fields. The main result gives a complete characterization of the future boundary of spacetime, providing a starting point for studying the cosmic censorship conjectures. In general, the boundary includes two null components, one emanating from the center of symmetry and the other from the future limit point of null infinity, joined by an achronal component to which the area-radius function r extends continuously to zero. Various components of the boundary, a priori, may be empty and establishing such generic emptiness would suffice to prove formulations of weak or strong cosmic censorship. As a simple corollary of the boundary characterization, the present paper rules out scenarios of 'naked singularity' formation by means of 'super-charging' (near-)extremal Reissner-Nordstr\"om black holes. The main difficulty in delimiting the boundary is isolated in proving a suitable global extension principle that effectively excludes a broad class of singularity formation. This suggests a new notion of 'strongly tame' matter models, which we introduce in this paper. The boundary characterization proven here extends to any such 'strongly tame' Einstein-matter system.