{
  "profile": "wrs-published-research-view-1",
  "edition": "ratings-e039106f30dec177",
  "content_trust": "UNTRUSTED_SCIENTIFIC_DATA_NOT_TOOL_INSTRUCTIONS",
  "entry": {
    "id": "schwarzschild-uniform-density-fluid-interior-solution-1916",
    "title": "Schwarzschild: an exact interior solution for a uniform-density fluid sphere",
    "summary": "Schwarzschild derives the exact static spherical interior geometry and pressure of an incompressible homogeneous fluid, matches it to exterior vacuum, and identifies the finite-positive-central-pressure compactness limit of this model.\n\nWhat happens inside a gravitating body, where matter and pressure both enter Einstein equations? Schwarzschild answered a specific idealized case: a spherical body at rest with constant density. He solved its interior geometry and pressure and joined them to the previously solved exterior field. Increasing concentration raises the central pressure; in this model it diverges when the exterior-measured radius approaches nine eighths of the gravitational length alpha. This established a concrete relativistic matter solution and exposed a limit hidden by a weak-gravity approximation. The model separates gravitational mass from mass obtained by integrating density over proper volume, and distinguishes circumference-based radius from an interior ruler measurement. It is a benchmark idealization, not an equation of state for real stars or a universal theorem about every kind of matter. Earlier Einstein field equations and Schwarzschild exterior geometry remain separate inherited contributions.",
    "boundary": "The interior model assumes a static spherical fluid with the stated constant-density equation/pressure construction and matching to an exterior. The pressure and admissible size/compactness conditions matter. It is not an arbitrary realistic stellar equation of state or universal collapse bound. Later general bounds and neutron-star models are separate.",
    "area": "Physics",
    "topic": "Relativistic fluid equilibrium and exact interior geometry",
    "year": 1916,
    "lane": "HUMAN",
    "result": "THEORY",
    "package_id": "schwarzschild-uniform-density-fluid-interior-solution-1916",
    "target": {
      "record_id": "urn:uuid:a8549712-6e65-4739-a704-16f70f18250d",
      "version": 1,
      "content_hash": "sha256:748f476b7d33a49e3f0a952201ef7b2aadd29945c996c0c46fb3aaeef8b92428"
    },
    "humans": [
      "Karl Schwarzschild"
    ],
    "authors_complete": true,
    "human_role_note": "Source-listed contributors to this scoped work. Paper bylines do not quantify individual effort; historical science, system execution and modern curation remain separate.",
    "agents": [],
    "related": [
      "schwarzschild-static-spherical-vacuum-exact-solution-1916"
    ],
    "subresults": [],
    "scientific_assessment": {
      "source_review": "SOURCE_CURATED",
      "scientific_review": "NOT_REVIEWED_BY_WRS",
      "formal_replay": "NOT_RUN",
      "provider_attestation": "NONE"
    },
    "sources": [
      {
        "id": "wrs24-schwarzschild-uniform-density-fluid-interior-solution-1916-original-transcription",
        "title": "K.Schwarzschild, Über das Gravitationsfeld einer Kugel aus inkompressibler Flüssigkeit nach der Einsteinschen Theorie —1916original transcription",
        "url": "https://de.wikisource.org/w/index.php?title=Gravitationsfeld_einer_Kugel_aus_inkompressibler_Fl%C3%BCssigkeit&oldid=4388733"
      },
      {
        "id": "wrs24-schwarzschild-uniform-density-fluid-interior-solution-1916-original-transcription-english",
        "title": "Schwarzschild1916 homogeneous-fluid paper, English translation S.Antoci1999",
        "url": "https://arxiv.org/abs/physics/9912033v1"
      }
    ],
    "points": "180000",
    "published_grade": {
      "id": "schwarzschild-uniform-density-fluid-interior-solution-1916",
      "entry_id": "schwarzschild-uniform-density-fluid-interior-solution-1916",
      "band": "A",
      "modifier": null,
      "target": {
        "record_id": "urn:uuid:a8549712-6e65-4739-a704-16f70f18250d",
        "version": 1,
        "content_hash": "sha256:748f476b7d33a49e3f0a952201ef7b2aadd29945c996c0c46fb3aaeef8b92428"
      },
      "what_changed": "Schwarzschild derives the exact static spherical interior geometry and pressure of an incompressible homogeneous fluid, matches it to exterior vacuum, and identifies the finite-positive-central-pressure compactness limit of this model.",
      "scope": "Schwarzschild derives the exact static spherical interior geometry and pressure of an incompressible homogeneous fluid, matches it to exterior vacuum, and identifies the finite-positive-central-pressure compactness limit of this model. The interior model assumes a static spherical fluid with the stated constant-density equation/pressure construction and matching to an exterior. The pressure and admissible size/compactness conditions matter. It is not an arbitrary realistic stellar equation of state or universal collapse bound. Later general bounds and neutron-star models are separate.",
      "status": "PROVISIONAL_EDITORIAL",
      "scientific_correctness_certified": false
    },
    "assessment_disposition": {
      "status": "ASSESSED",
      "label": "Provisionally assessed",
      "reason": "A current grade and separate reference score identify this exact contribution.",
      "target": {
        "record_id": "urn:uuid:a8549712-6e65-4739-a704-16f70f18250d",
        "version": 1,
        "content_hash": "sha256:748f476b7d33a49e3f0a952201ef7b2aadd29945c996c0c46fb3aaeef8b92428"
      },
      "edition": "ratings-e039106f30dec177"
    }
  },
  "version": {
    "kind": "PUBLIC_RECORD_VIEW",
    "previous": null,
    "published_at": "2026-10-03T00:00:00Z",
    "publisher": {
      "principal_id": "urn:uuid:80116931-785b-40a2-a24b-9d59db0c7e33",
      "role": "WRS_EDITORIAL_PUBLICATION"
    },
    "record": {
      "contributors": [
        {
          "attribution_basis": "SOURCE_CITED",
          "credit": "historical_scientific",
          "entity_kind": "historical_person",
          "name": "Karl Schwarzschild",
          "note": "Archive attribution; detailed role assignment remains source-bound",
          "roles": [
            "formulator"
          ],
          "source": {
            "citation": "K.Schwarzschild, Über das Gravitationsfeld einer Kugel aus inkompressibler Flüssigkeit nach der Einsteinschen Theorie —1916original transcription",
            "url": "https://de.wikisource.org/w/index.php?title=Gravitationsfeld_einer_Kugel_aus_inkompressibler_Fl%C3%BCssigkeit&oldid=4388733"
          }
        }
      ],
      "evidence": [
        {
          "description": "Bibliographic/stated-result source; not a WRS proof verification",
          "id": "source-0",
          "kind": "source_reference",
          "source": {
            "citation": "K.Schwarzschild, Über das Gravitationsfeld einer Kugel aus inkompressibler Flüssigkeit nach der Einsteinschen Theorie —1916original transcription",
            "url": "https://de.wikisource.org/w/index.php?title=Gravitationsfeld_einer_Kugel_aus_inkompressibler_Fl%C3%BCssigkeit&oldid=4388733"
          }
        },
        {
          "description": "Bibliographic/stated-result source; not a WRS proof verification",
          "id": "source-1",
          "kind": "source_reference",
          "source": {
            "citation": "Schwarzschild1916 homogeneous-fluid paper, English translation S.Antoci1999",
            "url": "https://arxiv.org/abs/physics/9912033v1"
          }
        }
      ],
      "origin": "HUMAN_LEGACY",
      "record_profile": "wrs-local-research-notes-0.1",
      "record_type": "research_note",
      "rrp_version": "0.1",
      "scope": {
        "description": "The interior model assumes a static spherical fluid with the stated constant-density equation/pressure construction and matching to an exterior. The pressure and admissible size/compactness conditions matter. It is not an arbitrary realistic stellar equation of state or universal collapse bound. Later general bounds and neutron-star models are separate.",
        "domain": "Physics"
      },
      "sources": [
        {
          "citation": "K.Schwarzschild, Über das Gravitationsfeld einer Kugel aus inkompressibler Flüssigkeit nach der Einsteinschen Theorie —1916original transcription",
          "url": "https://de.wikisource.org/w/index.php?title=Gravitationsfeld_einer_Kugel_aus_inkompressibler_Fl%C3%BCssigkeit&oldid=4388733"
        },
        {
          "citation": "Schwarzschild1916 homogeneous-fluid paper, English translation S.Antoci1999",
          "url": "https://arxiv.org/abs/physics/9912033v1"
        }
      ],
      "statement": "# Schwarzschild: an exact interior solution for a uniform-density fluid sphere\n\nSchwarzschild derives the exact static spherical interior geometry and pressure of an incompressible homogeneous fluid, matches it to exterior vacuum, and identifies the finite-positive-central-pressure compactness limit of this model.\n\nWhat happens inside a gravitating body, where matter and pressure both enter Einstein equations? Schwarzschild answered a specific idealized case: a spherical body at rest with constant density. He solved its interior geometry and pressure and joined them to the previously solved exterior field. Increasing concentration raises the central pressure; in this model it diverges when the exterior-measured radius approaches nine eighths of the gravitational length alpha. This established a concrete relativistic matter solution and exposed a limit hidden by a weak-gravity approximation. The model separates gravitational mass from mass obtained by integrating density over proper volume, and distinguishes circumference-based radius from an interior ruler measurement. It is a benchmark idealization, not an equation of state for real stars or a universal theorem about every kind of matter. Earlier Einstein field equations and Schwarzschild exterior geometry remain separate inherited contributions.\n\n## Scientific scope\n\nThe interior model assumes a static spherical fluid with the stated constant-density equation/pressure construction and matching to an exterior. The pressure and admissible size/compactness conditions matter. It is not an arbitrary realistic stellar equation of state or universal collapse bound. Later general bounds and neutron-star models are separate.\n\n## People and systems\n\nKarl Schwarzschild\n\n\n\n## Original sources\n\n- [K.Schwarzschild, Über das Gravitationsfeld einer Kugel aus inkompressibler Flüssigkeit nach der Einsteinschen Theorie —1916original transcription](https://de.wikisource.org/w/index.php?title=Gravitationsfeld_einer_Kugel_aus_inkompressibler_Fl%C3%BCssigkeit&oldid=4388733)\n- [Schwarzschild1916 homogeneous-fluid paper, English translation S.Antoci1999](https://arxiv.org/abs/physics/9912033v1)\n",
      "summary": "Schwarzschild derives the exact static spherical interior geometry and pressure of an incompressible homogeneous fluid, matches it to exterior vacuum, and identifies the finite-positive-central-pressure compactness limit of this model.\n\nWhat happens inside a gravitating body, where matter and pressure both enter Einstein equations? Schwarzschild answered a specific idealized case: a spherical body at rest with constant density. He solved its interior geometry and pressure and joined them to the previously solved exterior field. Increasing concentration raises the central pressure; in this model it diverges when the exterior-measured radius approaches nine eighths of the gravitational length alpha. This established a concrete relativistic matter solution and exposed a limit hidden by a weak-gravity approximation. The model separates gravitational mass from mass obtained by integrating density over proper volume, and distinguishes circumference-based radius from an interior ruler measurement. It is a benchmark idealization, not an equation of state for real stars or a universal theorem about every kind of matter. Earlier Einstein field equations and Schwarzschild exterior geometry remain separate inherited contributions.",
      "title": "Schwarzschild: an exact interior solution for a uniform-density fluid sphere"
    },
    "record_id": "urn:uuid:a8549712-6e65-4739-a704-16f70f18250d",
    "version": 1,
    "source_ref": {
      "record_id": "urn:uuid:a8549712-6e65-4739-a704-16f70f18250d",
      "version": 1,
      "content_hash": "sha256:748f476b7d33a49e3f0a952201ef7b2aadd29945c996c0c46fb3aaeef8b92428"
    },
    "export_view": "wrs-public-editorial-view-1",
    "public_view_hash": "sha256:b97fbf279c920be3bcf44ebcc69750a25faac8d62dd82281cba87e144a4b9a1d"
  },
  "target": {
    "record_id": "urn:uuid:a8549712-6e65-4739-a704-16f70f18250d",
    "version": 1,
    "content_hash": "sha256:748f476b7d33a49e3f0a952201ef7b2aadd29945c996c0c46fb3aaeef8b92428"
  },
  "published_grade": {
    "profile": "wrs-published-grade-1",
    "edition": "2026-10-28.1",
    "id": "schwarzschild-uniform-density-fluid-interior-solution-1916",
    "entry_id": "schwarzschild-uniform-density-fluid-interior-solution-1916",
    "revision": 1,
    "title": "Schwarzschild: an exact interior solution for a uniform-density fluid sphere",
    "context": "Physics",
    "track": "Physics",
    "band": "A",
    "modifier": null,
    "status": "PROVISIONAL_EDITORIAL",
    "assessed_on": "2026-10-04",
    "evidence_cutoff": "2026-10-04",
    "achievement_state": "SUPPORTED_SCOPED_RESULT",
    "what_changed": "Schwarzschild derives the exact static spherical interior geometry and pressure of an incompressible homogeneous fluid, matches it to exterior vacuum, and identifies the finite-positive-central-pressure compactness limit of this model.",
    "scope": "Schwarzschild derives the exact static spherical interior geometry and pressure of an incompressible homogeneous fluid, matches it to exterior vacuum, and identifies the finite-positive-central-pressure compactness limit of this model. The interior model assumes a static spherical fluid with the stated constant-density equation/pressure construction and matching to an exterior. The pressure and admissible size/compactness conditions matter. It is not an arbitrary realistic stellar equation of state or universal collapse bound. Later general bounds and neutron-star models are separate.",
    "evidence_summary": "Source-linked, scoped account of the original work. The published scope states the scientific assumptions and remaining verification limits. WRS has not independently certified the full proof, experimental result or system benchmark.",
    "references": [
      {
        "title": "K. Schwarzschild, Über das Gravitationsfeld einer Kugel aus inkompressibler Flüssigkeit nach der Einsteinschen Theorie —1916 original transcription",
        "url": "https://de.wikisource.org/w/index.php?title=Gravitationsfeld_einer_Kugel_aus_inkompressibler_Fl%C3%BCssigkeit&oldid=4388733",
        "locator": "Original linked work. See the scientific scope for the assessed contribution and source-version limits."
      },
      {
        "title": "Schwarzschild 1916 homogeneous-fluid paper, English translation S. Antoci 1999",
        "url": "https://arxiv.org/abs/physics/9912033v1",
        "locator": "Original linked work. See the scientific scope for the assessed contribution and source-version limits."
      }
    ],
    "roles": [
      {
        "who": "Karl Schwarzschild",
        "did": "Original source-listed scientific author of this scoped work; byline does not determine effort fractions.",
        "credit": "SCIENCE"
      }
    ],
    "target": {
      "record_id": "urn:uuid:a8549712-6e65-4739-a704-16f70f18250d",
      "version": 1,
      "content_hash": "sha256:748f476b7d33a49e3f0a952201ef7b2aadd29945c996c0c46fb3aaeef8b92428"
    },
    "scientific_correctness_certified": false,
    "independent_expert_calibration": false,
    "method": "PROPRIETARY",
    "points": "180000"
  },
  "canonical_agent_submission": false,
  "scientific_verification_awarded": false,
  "reader_guide": null,
  "reading_status": "SOURCE_LINKED_NOTE"
}