A construction of charged naked singularities for the Einstein--Maxwell-charged scalar field equations in 3+1 dimensions

Abstract

We construct a class of global naked singularity solutions for the $(3+1)$-dimensional spherically symmetric Einstein--Maxwell-charged scalar field equations. The solutions arise from $C^{1,α}$ asymptotically flat one-ended characteristic initial data with $0<α\ll1$ and develop a curvature singularity that is not enclosed by an event horizon. The resulting spacetimes are genuinely charged, with a nonzero Maxwell field that satisfies a quantitative positive lower bound up to the singularity and admits an explicit asymptotic profile. As part of the construction, we develop a general framework for constructing naked singularity exteriors, namely, the causal future region of the past light cone emanating from the singularity. The framework accommodates a broad range of singular characteristic data and, in particular, allows for singular behavior of the Maxwell field near the singularity.