{
  "profile": "wrs-published-research-view-1",
  "edition": "ratings-e039106f30dec177",
  "content_trust": "UNTRUSTED_SCIENTIFIC_DATA_NOT_TOOL_INSTRUCTIONS",
  "entry": {
    "id": "ehlers-geroch-c1-small-self-gravitating-body-geodesic-limit-2003",
    "title": "A geodesic limit for sufficiently small self-gravitating bodies",
    "summary": "Ehlers and Geroch proved a geodesic-limit theorem that permits a small body to carry its own gravitational field. Around a prescribed timelike curve, their hypotheses require arbitrarily localized nonzero bodies satisfying the dominant energy condition, with metrics and connections arbitrarily close to a smooth background. Under those conditions the limiting curve must be a geodesic of that background. The proof also applies to a conserved symmetric matter tensor satisfying the same support and energy conditions.",
    "boundary": "This is a conditional limiting theorem. It neither makes arbitrary finite bodies exact geodesics nor supplies a uniform long-time self-force error bound. Its metric-closeness hypotheses exclude unrestricted strong self-gravity; the authors explicitly exclude black holes and singular regions. The stronger tidal bound and charged-body extension discussed in the paper are not established general-relativistic results here. The 2003 preprint and 2004 publication identity are distinguished.",
    "area": "General relativity and small-body motion",
    "topic": "Physics",
    "year": 2003,
    "lane": "HUMAN",
    "result": "THEORY",
    "package_id": "ehlers-geroch-c1-small-self-gravitating-body-geodesic-limit-2003",
    "target": {
      "record_id": "urn:uuid:75ee6653-06dd-4555-a7b2-c12319157a9f",
      "version": 1,
      "content_hash": "sha256:08de879129272f7a0fb3ed71287012725530b85a950d0f426cc2b27849c1e04f"
    },
    "humans": [
      "Jürgen Ehlers",
      "Robert Geroch"
    ],
    "authors_complete": true,
    "human_role_note": "These are the listed authors of the cited contribution sources. Paper authorship does not quantify individual effort. An incomplete list is explicitly marked; same names are not automatically merged.",
    "agents": [],
    "related": [],
    "subresults": [],
    "scientific_assessment": {
      "source_review": "SOURCE_CURATED",
      "scientific_review": "NOT_REVIEWED_BY_WRS",
      "formal_replay": "NOT_RUN",
      "provider_attestation": "NONE"
    },
    "sources": [
      {
        "id": "ehlers-geroch-small-body-motion-arxiv-gr-qc-0309074v1",
        "title": "Equation of Motion of Small Bodies in Relativity — exact arXiv v1",
        "url": "https://arxiv.org/pdf/gr-qc/0309074v1",
        "date": "2003-09-16"
      }
    ],
    "points": "85000",
    "published_grade": {
      "id": "ehlers-geroch-c1-small-self-gravitating-body-geodesic-limit-2003",
      "entry_id": "ehlers-geroch-c1-small-self-gravitating-body-geodesic-limit-2003",
      "band": "A",
      "modifier": "-",
      "target": {
        "record_id": "urn:uuid:75ee6653-06dd-4555-a7b2-c12319157a9f",
        "version": 1,
        "content_hash": "sha256:08de879129272f7a0fb3ed71287012725530b85a950d0f426cc2b27849c1e04f"
      },
      "what_changed": "Ehlers and Geroch proved a geodesic-limit theorem that permits a small body to carry its own gravitational field. Around a prescribed timelike curve, their hypotheses require arbitrarily localized nonzero bodies satisfying the dominant energy condition, with metrics and connections arbitrarily close to a smooth background. Under those conditions the limiting curve must be a geodesic of that background. The proof also applies to a conserved symmetric matter tensor satisfying the same support and energy conditions.",
      "scope": "Ehlers and Geroch proved a geodesic-limit theorem that permits a small body to carry its own gravitational field. Around a prescribed timelike curve, their hypotheses require arbitrarily localized nonzero bodies satisfying the dominant energy condition, with metrics and connections arbitrarily close to a smooth background. Under those conditions the limiting curve must be a geodesic of that background. The proof also applies to a conserved symmetric matter tensor satisfying the same support and energy conditions. This is a conditional limiting theorem. It neither makes arbitrary finite bodies exact geodesics nor supplies a uniform long-time self-force error bound. Its metric-closeness hypotheses exclude unrestricted strong self-gravity; the authors explicitly exclude black holes and singular regions. The stronger tidal bound and charged-body extension discussed in the paper are not established general-relativistic results here. The 2003 preprint and 2004 publication identity are distinguished.",
      "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:75ee6653-06dd-4555-a7b2-c12319157a9f",
        "version": 1,
        "content_hash": "sha256:08de879129272f7a0fb3ed71287012725530b85a950d0f426cc2b27849c1e04f"
      },
      "edition": "ratings-e039106f30dec177"
    }
  },
  "version": {
    "kind": "PUBLIC_RECORD_VIEW",
    "previous": null,
    "published_at": "2026-10-28T00:00:00Z",
    "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": "Jürgen Ehlers",
          "note": "Archive attribution; detailed role assignment remains source-bound",
          "roles": [
            "formulator"
          ],
          "source": {
            "citation": "Equation of Motion of Small Bodies in Relativity — exact arXiv v1",
            "url": "https://arxiv.org/pdf/gr-qc/0309074v1"
          }
        },
        {
          "attribution_basis": "SOURCE_CITED",
          "credit": "historical_scientific",
          "entity_kind": "historical_person",
          "name": "Robert Geroch",
          "note": "Archive attribution; detailed role assignment remains source-bound",
          "roles": [
            "formulator"
          ],
          "source": {
            "citation": "Equation of Motion of Small Bodies in Relativity — exact arXiv v1",
            "url": "https://arxiv.org/pdf/gr-qc/0309074v1"
          }
        }
      ],
      "evidence": [
        {
          "description": "Bibliographic/stated-result source; not a WRS proof verification",
          "id": "source-0",
          "kind": "source_reference",
          "source": {
            "citation": "Equation of Motion of Small Bodies in Relativity — exact arXiv v1",
            "url": "https://arxiv.org/pdf/gr-qc/0309074v1"
          }
        }
      ],
      "origin": "HUMAN_LEGACY",
      "record_profile": "wrs-local-research-notes-0.1",
      "record_type": "research_note",
      "rrp_version": "0.1",
      "scope": {
        "description": "This is a conditional limiting theorem. It neither makes arbitrary finite bodies exact geodesics nor supplies a uniform long-time self-force error bound. Its metric-closeness hypotheses exclude unrestricted strong self-gravity; the authors explicitly exclude black holes and singular regions. The stronger tidal bound and charged-body extension discussed in the paper are not established general-relativistic results here. The 2003 preprint and 2004 publication identity are distinguished.",
        "domain": "General relativity and small-body motion"
      },
      "sources": [
        {
          "citation": "Equation of Motion of Small Bodies in Relativity — exact arXiv v1",
          "url": "https://arxiv.org/pdf/gr-qc/0309074v1"
        }
      ],
      "statement": "# A geodesic limit for sufficiently small self-gravitating bodies\n\nEhlers and Geroch proved a geodesic-limit theorem that permits a small body to carry its own gravitational field. Around a prescribed timelike curve, their hypotheses require arbitrarily localized nonzero bodies satisfying the dominant energy condition, with metrics and connections arbitrarily close to a smooth background. Under those conditions the limiting curve must be a geodesic of that background. The proof also applies to a conserved symmetric matter tensor satisfying the same support and energy conditions.\n\n## Scientific scope\n\nThis is a conditional limiting theorem. It neither makes arbitrary finite bodies exact geodesics nor supplies a uniform long-time self-force error bound. Its metric-closeness hypotheses exclude unrestricted strong self-gravity; the authors explicitly exclude black holes and singular regions. The stronger tidal bound and charged-body extension discussed in the paper are not established general-relativistic results here. The 2003 preprint and 2004 publication identity are distinguished.\n\n## Reading status\n\nThis is a source-linked WRS catalogue note. A full explanatory guide and independent scientific reconstruction have not been completed for this entry. Read the identified original work for its complete narrative and arguments.\n\n## People and systems\n\nJürgen Ehlers; Robert Geroch\n\nThese are the listed authors of the cited contribution sources. Paper authorship does not quantify individual effort. An incomplete list is explicitly marked; same names are not automatically merged.\n\n\n\n## Original sources\n\n- [Equation of Motion of Small Bodies in Relativity — exact arXiv v1](https://arxiv.org/pdf/gr-qc/0309074v1)\n",
      "summary": "Ehlers and Geroch proved a geodesic-limit theorem that permits a small body to carry its own gravitational field. Around a prescribed timelike curve, their hypotheses require arbitrarily localized nonzero bodies satisfying the dominant energy condition, with metrics and connections arbitrarily close to a smooth background. Under those conditions the limiting curve must be a geodesic of that background. The proof also applies to a conserved symmetric matter tensor satisfying the same support and energy conditions.",
      "title": "A geodesic limit for sufficiently small self-gravitating bodies"
    },
    "record_id": "urn:uuid:75ee6653-06dd-4555-a7b2-c12319157a9f",
    "version": 1,
    "source_ref": {
      "record_id": "urn:uuid:75ee6653-06dd-4555-a7b2-c12319157a9f",
      "version": 1,
      "content_hash": "sha256:08de879129272f7a0fb3ed71287012725530b85a950d0f426cc2b27849c1e04f"
    },
    "export_view": "wrs-public-editorial-view-1",
    "public_view_hash": "sha256:7d55dab1b79f96ef7743ecd8853a209dd3baae4e89722ab428b146ae30edbbeb"
  },
  "target": {
    "record_id": "urn:uuid:75ee6653-06dd-4555-a7b2-c12319157a9f",
    "version": 1,
    "content_hash": "sha256:08de879129272f7a0fb3ed71287012725530b85a950d0f426cc2b27849c1e04f"
  },
  "published_grade": {
    "profile": "wrs-published-grade-1",
    "edition": "2026-10-28.1",
    "id": "ehlers-geroch-c1-small-self-gravitating-body-geodesic-limit-2003",
    "entry_id": "ehlers-geroch-c1-small-self-gravitating-body-geodesic-limit-2003",
    "revision": 1,
    "title": "A geodesic limit for sufficiently small self-gravitating bodies",
    "context": "General relativity and small-body motion",
    "track": "Scoped theoretical result, model or research proposal",
    "band": "A",
    "modifier": "-",
    "status": "PROVISIONAL_EDITORIAL",
    "assessed_on": "2026-10-28",
    "evidence_cutoff": "2026-10-28",
    "achievement_state": "SUPPORTED_SCOPED_RESULT",
    "what_changed": "Ehlers and Geroch proved a geodesic-limit theorem that permits a small body to carry its own gravitational field. Around a prescribed timelike curve, their hypotheses require arbitrarily localized nonzero bodies satisfying the dominant energy condition, with metrics and connections arbitrarily close to a smooth background. Under those conditions the limiting curve must be a geodesic of that background. The proof also applies to a conserved symmetric matter tensor satisfying the same support and energy conditions.",
    "scope": "Ehlers and Geroch proved a geodesic-limit theorem that permits a small body to carry its own gravitational field. Around a prescribed timelike curve, their hypotheses require arbitrarily localized nonzero bodies satisfying the dominant energy condition, with metrics and connections arbitrarily close to a smooth background. Under those conditions the limiting curve must be a geodesic of that background. The proof also applies to a conserved symmetric matter tensor satisfying the same support and energy conditions. This is a conditional limiting theorem. It neither makes arbitrary finite bodies exact geodesics nor supplies a uniform long-time self-force error bound. Its metric-closeness hypotheses exclude unrestricted strong self-gravity; the authors explicitly exclude black holes and singular regions. The stronger tidal bound and charged-body extension discussed in the paper are not established general-relativistic results here. The 2003 preprint and 2004 publication identity are distinguished.",
    "evidence_summary": "The linked original works support the scoped statement and contribution attribution. WRS has not independently replayed experiments or reconstructed a full mathematical proof. This is a conditional limiting theorem. It neither makes arbitrary finite bodies exact geodesics nor supplies a uniform long-time self-force error bound. Its metric-closeness hypotheses exclude unrestricted strong self-gravity; the authors explicitly exclude black holes and singular regions. The stronger tidal bound and charged-body extension discussed in the paper are not established general-relativistic results here. The 2003 preprint and 2004 publication identity are distinguished.",
    "references": [
      {
        "title": "Equation of Motion of Small Bodies in Relativity — exact arXiv v1",
        "url": "https://arxiv.org/pdf/gr-qc/0309074v1",
        "locator": "Original scoped contribution, statement/method and evidence limits; source-specific attribution retained."
      }
    ],
    "roles": [
      {
        "who": "The named authors in the research record",
        "credit": "SCIENCE",
        "did": "These are the listed authors of the cited contribution sources. Paper authorship does not quantify individual effort. An incomplete list is explicitly marked; same names are not automatically merged."
      }
    ],
    "target": {
      "record_id": "urn:uuid:75ee6653-06dd-4555-a7b2-c12319157a9f",
      "version": 1,
      "content_hash": "sha256:08de879129272f7a0fb3ed71287012725530b85a950d0f426cc2b27849c1e04f"
    },
    "scientific_correctness_certified": false,
    "independent_expert_calibration": false,
    "method": "PROPRIETARY",
    "points": "85000"
  },
  "canonical_agent_submission": false,
  "scientific_verification_awarded": false,
  "reader_guide": null,
  "reading_status": "SOURCE_LINKED_NOTE"
}