{
  "abstract": "We examine whether the hyperbolic rapidity parametrization developed in earlier work for the interior metric of a Schwarzschild black hole can also parametrize the electrostatic field of a charged particle described by a Gaussian envelope. The construction is motivated by the observation that the Lorentz-contracted width of a Gaussian wavepacket, σ(φ) = σ₀ sech φ, acts as a linear amplitude whose Born-like conjugate square matches the functional form of the interior metric of a Schwarzschild black hole, r/rₛ = sech² β. Treating the Compton width σ₀ as a boundary between an exterior Coulomb regime and an interior regime, we clarify how the linear exterior coordinate rₑₓₜ(φ) = σ₀ cosh φ combines with the inverse-square Coulomb law to yield Eₑₓₜ ∝ sech² φ, while the interior profile is algebraically equivalent to that of a uniformly charged sphere. The electrostatic self-energy of this configuration is (3/5)αmₑc², where α is the fine-structure constant. We also observe that the ratio of the classical electron radius rₑ = ασ₀ to the dynamical Compton horizon σ(φ) equals α cosh φ in a frame of rapidity φ, a purely kinematic identity that reduces to α at rest. Finally, using the exterior gravitational metric rₑₓₜ = rₛ cosh² β to derive the exact Schwarzschild lapse factor √(1 − rₛ/rₑₓₜ) = tanh β in the Tolman temperature, we justify the physical domain |β| > 0 on which ψ(β) = sech β satisfies a differential identity algebraically identical to the Ginzburg–Landau field equation. The mathematical identities are exact; the physical interpretations are offered as conjectures.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": null,
  "author_total": 1,
  "authors": [
    {
      "name": "Rodrigo Silva Barros"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/aw2yphwfdh48s.bib",
  "cited_by": 0,
  "doi": "10.5281/zenodo.23651339",
  "fulltext_url": null,
  "id": "aw2yphwfdh48s",
  "issns": [],
  "landing_url": "https://zenodo.org/records/23651339",
  "language": "eng",
  "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": null,
  "pdf_url": "https://zenodo.org/api/records/23651339/files/Hyperbolic%20Rapidity%20Parametrization%20of%20the%20Coulomb%20Field.pdf/content",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-25",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/aw2yphwfdh48s.ris",
  "sources": [
    {
      "first_seen": "2026-11-08T12:20:58Z",
      "native_id": "23651339",
      "source": "zenodo",
      "url": "https://zenodo.org/records/23651339"
    }
  ],
  "subjects": [],
  "title": "Hyperbolic Rapidity Parametrization of the Coulomb Field: Gaussian Envelope, Two-Regime Electrostatics, and the Fine-Structure Constant as a Rest-Frame Ratio",
  "title_text": "Hyperbolic Rapidity Parametrization of the Coulomb Field: Gaussian Envelope, Two-Regime Electrostatics, and the Fine-Structure Constant as a Rest-Frame Ratio",
  "type": "preprint",
  "updated_at": "2026-11-08T12:20:58Z",
  "url": "https://research.draconitic.com/paper/aw2yphwfdh48s",
  "venue": "Zenodo",
  "versions": []
}