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 C1,α asymptotically flat one-ended characteristic initial data with 0<α≪1 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.
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BibTeX
@misc{zheng2026construction,
title = {{A construction of charged naked singularities for the Einstein--Maxwell-charged scalar field equations in 3+1 dimensions}},
author = {Weihao Zheng},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.33168},
eprint = {2609.33168},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.33168},
}
RIS
TY - UNPB
TI - A construction of charged naked singularities for the Einstein--Maxwell-charged scalar field equations in 3+1 dimensions
AU - Weihao Zheng
PY - 2026
DA - 2026/09/27
PB - arXiv
DO - 10.48550/arxiv.2609.33168
UR - https://arxiv.org/abs/2609.33168
AB - 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≪1 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.
ER -