{
  "abstract": "We prove a new extension principle for the spherically symmetric Einstein--Maxwell--charged scalar field system. Rather than imposing conditions for mass ratio $2m/r$ as in Christodoulou's small-mass-ratio criterion or as in An--Chen--Singh's proof [1] with $2m/r<3/8$, here we work through a proposal by An-Tan [2] with finite Doppler exponent (blueshift). By conducting two successive blow-up analyses, followed by a stationary comparison and a rigidity argument, we establish the uniform boundness of $α'$ with $α'=\\partial_vα/\\partial_vr$ and $α=\\partial_v(rϕ)/\\partial_vr$. This provides the desired extension principle in An-Tan [2] and completes the picture of weak cosmic censorship developed therein. As we were about to release our preprint, Cicortas communicated to us that together with his collaborators, they concomitantly used a different approach to obtain the corresponding extension principle with finite blueshift (Doppler exponent) for the uncharged Einstein-scalar field system. Hence, we decided to put the current paper as an appendix to An-Tan [2], thereby completing the proof of the weak cosmic censorship for the Einstein-Maxwell-charged scalar field system. At the same time, we are working with Cicortas and his collaborators to write a new preprint containing both approaches for the Einstein-scalar field system.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.20469",
  "author_total": 3,
  "authors": [
    {
      "name": "Xinliang An"
    },
    {
      "name": "Haoyang Chen"
    },
    {
      "name": "Taoran He"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/8gkyxcm17mz0x.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.20469",
  "fulltext_url": null,
  "id": "8gkyxcm17mz0x",
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  "landing_url": "https://arxiv.org/abs/2610.20469",
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  "licence": "CC-BY-NC-ND-4.0",
  "licence_label": "CC BY-NC-ND 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by-nc-nd/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
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      "3106|Black Holes and Theoretical Physics"
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  "openalex": "W7222049233",
  "pdf_url": "https://arxiv.org/pdf/2610.20469",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-14",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/8gkyxcm17mz0x.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:31Z",
      "native_id": "2610.20469",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.20469"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.DG",
      "subfield": "geometry-topology"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math-ph",
      "subfield": "mathematical-physics"
    },
    {
      "field": "physics",
      "origin": "arxiv:gr-qc",
      "subfield": "gravitation"
    }
  ],
  "title": "An extension principle for Einstein-Maxwell-charged scalar field system with finite Doppler exponent",
  "title_text": "An extension principle for Einstein-Maxwell-charged scalar field system with finite Doppler exponent",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:35Z",
  "url": "https://research.draconitic.com/paper/8gkyxcm17mz0x",
  "venue": "arXiv",
  "versions": []
}