{
  "abstract": "Charge-dependent scalarization of the Einstein–Euler–Heisenberg (EEH) black hole is carried out in the EEH-scalar theory by introducing an exponential scalar coupling with coupling constant $$\\alpha $$ α to the Maxwell and nonlinear electrodynamic terms. The bald black hole (EEHBH) is described by mass M and arbitrary magnetic charge q and has a single horizon when choosing the action parameter $$\\mu =0.3$$ μ = 0.3 . Here, we find the critical onset charge $$q_c=r_+^2/\\sqrt{2\\mu }$$ q c = r + 2 / 2 μ with $$r_+(M,q_c)$$ r + ( M , q c ) the outer horizon radius from the resonance condition. The spontaneous scalarization ( $$\\alpha ^+$$ α + ) of this black hole is available for charge $$0<q< q_c=1.115$$ 0 < q < q c = 1.115 for $$M=1$$ M = 1 and $$\\mu =0.3$$ μ = 0.3 , with positive $$\\alpha $$ α , whereas its new scalarization ( $$\\alpha ^-$$ α - ) occurs for $$q> q_c$$ q > q c and negative $$\\alpha $$ α . The former case of $$q=0.5$$ q = 0.5 implies infinite branches of scalarized EEHBHs but its fundamental branch ( $$n=0$$ n = 0 ) is stable against the $$l=0$$ l = 0 modes considered here, while for $$q=2$$ q = 2 and $$q=20$$ q = 20 , one stable scalarized branch is found for each charge within the explored parameter ranges.",
  "abstract_shown": true,
  "affiliations": [
    "Hunan Institute of Technology",
    "Sogang University",
    "Jiangxi Normal University",
    "Nanchang University",
    "College of Physical Science and Technology, Yangzhou University"
  ],
  "article_type": null,
  "arxiv": null,
  "author_total": 5,
  "authors": [
    {
      "affs": [
        0
      ],
      "name": "Lina Zhang"
    },
    {
      "affs": [
        1
      ],
      "name": "Yun Soo Myung",
      "orcid": "0000-0001-6343-9959"
    },
    {
      "affs": [
        2
      ],
      "name": "De-Cheng Zou",
      "orcid": "0000-0001-9809-9210"
    },
    {
      "affs": [
        3
      ],
      "name": "Chao-Ming Zhang",
      "orcid": "0009-0006-1276-0236"
    },
    {
      "affs": [
        4
      ],
      "name": "Sheng-Yuan Li",
      "orcid": "0009-0003-2049-8520"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/8cb80q7704237.bib",
  "cited_by": 0,
  "doi": "10.1140/epjc/s10052-026-16436-y",
  "fulltext_url": null,
  "id": "8cb80q7704237",
  "issns": [
    "1434-6044",
    "1434-6052"
  ],
  "landing_url": "https://link.springer.com/10.1140/epjc/s10052-026-16436-y",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "https://creativecommons.org/licenses/by/4.0",
  "metadata_licence": null,
  "native_subjects": [
    [
      "openalex",
      "3106|Black Holes and Theoretical Physics"
    ]
  ],
  "openalex": "W7161573761",
  "pdf_url": "https://link.springer.com/content/pdf/10.1140/epjc/s10052-026-16436-y.pdf",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-12",
  "publisher": "Springer Science and Business Media LLC",
  "ris": "https://research.draconitic.com/paper/8cb80q7704237.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:18:04Z",
      "native_id": "10.1140/epjc/s10052-026-16436-y",
      "source": "crossref",
      "url": "https://link.springer.com/10.1140/epjc/s10052-026-16436-y"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "openalex:3106|Black Holes and Theoretical Physics",
      "subfield": "high-energy"
    }
  ],
  "title": "Charge-dependent scalarization of Einstein–Euler–Heisenberg black holes",
  "title_text": "Charge-dependent scalarization of Einstein–Euler–Heisenberg black holes",
  "type": "peer-reviewed",
  "updated_at": "2026-10-30T12:18:04Z",
  "url": "https://research.draconitic.com/paper/8cb80q7704237",
  "venue": "The European Physical Journal C",
  "versions": []
}