{
  "abstract": "Minimal Geometric Deformation (MGD) applied to a static Schwarzschild black hole seed generates a single decoupler function $h(r)$, obtained by solving the $θ$-sector field equations together with an equation of state. Once $h(r)$ is fixed, the resulting one-parameter family is controlled by the coupling strength $k$ through $F(r;k)=1+k\\,h(r)$. We show that, whenever the deformation develops a simple outermost root that crosses the seed horizon, the same fixed decoupler leads to two mutually exclusive branches associated with different global completions: on one side of the critical coupling the deformed metric preserves the seed horizon as a black hole, whereas on the other side the root $r_*>2M$ lies in the exterior and cannot be interpreted as an interior modification of the black hole geometry. We prove that this root forces a loss of Lorentzian signature on the interval $(2M,r_*)$, so that no smooth extension of the exterior metric through the seed horizon $r=2M$ exists once $r_*$ lies outside it. Within the static, spherically symmetric class considered here, the corresponding smooth Lorentzian completion is a two-ended wormhole obtained by excising $(2M,r_*)$ and doubling the region $r\\geq r_*$ across the minimal sphere $\\mathcal T=\\{r=r_*\\}$. No topology change of any single spacetime is claimed or required: $k>k_c$ and $k<k_c$ simply correspond to two different, non-diffeomorphic manifolds, and Lemma~1 below shows that the metric itself dictates which of the two is the admissible completion for a given $k$. We compute the second homology group of both completions explicitly, $H_2(Σ_{\\rm BH},\\mathcal H)=0$ for the black hole exterior relative to its horizon and $H_2(Σ_{\\rm WH})\\cong\\mathbb Z$ for the completed wormhole manifold, giving a discrete invariant that distinguishes the two branches.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.10102",
  "author_total": 4,
  "authors": [
    {
      "name": "Francisco Tello-Ortiz"
    },
    {
      "name": "Y. Gomez-Leyton"
    },
    {
      "name": "Vitalii Vertogradov"
    },
    {
      "name": "Jean Baez Cuevas"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/aqe5arg7ppwpc.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.10102",
  "fulltext_url": null,
  "id": "aqe5arg7ppwpc",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.10102",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "gr-qc"
    ],
    [
      "openalex",
      "3103|Cosmology and Gravitation Theories"
    ]
  ],
  "openalex": "W7212143177",
  "pdf_url": "https://arxiv.org/pdf/2609.10102",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-09",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/aqe5arg7ppwpc.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:20:12Z",
      "native_id": "2609.10102",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.10102"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:gr-qc",
      "subfield": "gravitation"
    }
  ],
  "title": "Black hole and wormhole branches in gravitational decoupling",
  "title_text": "Black hole and wormhole branches in gravitational decoupling",
  "type": "preprint",
  "updated_at": "2026-10-30T12:20:12Z",
  "url": "https://research.draconitic.com/paper/aqe5arg7ppwpc",
  "venue": "arXiv",
  "versions": []
}