{ "profile": "wrs-published-research-view-1", "edition": "ratings-e039106f30dec177", "content_trust": "UNTRUSTED_SCIENTIFIC_DATA_NOT_TOOL_INSTRUCTIONS", "entry": { "id": "oppenheimer-volkoff-ideal-neutron-equilibrium-1939", "title": "Oppenheimer and Volkoff: a relativistic neutron-core equilibrium model", "summary": "Oppenheimer and Volkoff formulate general-relativistic hydrostatic equilibrium for a static spherical fluid and apply it to an ideal cold neutron gas, finding a model-dependent maximum gravitational mass near 0.7 solar masses.\n\nPressure can support a compact star, but pressure and internal energy also affect gravity in relativity. The authors turn that balance into equations for a spherical star and numerically explore a simple cold neutron gas. The resulting sequence reaches a largest supported mass in that model. The reusable contribution is the equilibrium framework and an explicit demonstration that the material law matters; the historical ideal-gas number is not a measurement of every real neutron star.", "boundary": "The target is the 1939 static, spherical, isotropic perfect-fluid equilibrium formulation and its cold noninteracting neutron-gas application, with zero cosmological constant. Mass/pressure equations require an equation of state, regular central conditions, a pressure-free boundary and exterior matching. The reported about 0.7-solar-mass limit belongs to this ideal equation of state; it is not a universal bound for real neutron stars. Table I samples give a largest listed 0.71, while some web fractions are misread. Thermal energy and forces between neutrons are neglected in the ideal calculation. The authors explicitly acknowledge uncertain extrapolation above nuclear density and consider repulsive-interaction changes; their expectation that the number is near reality is not adopted. Stability is discussed through schematic free-energy reasoning, not an independently reconstructed general perturbation theorem. Numerical integrations, every table glyph and a global uniqueness argument were not replayed. Static equilibrium limits do not themselves supply a general dynamical collapse solution; the Snyder paper is separate. Tolman and earlier degeneracy theory retain credit.", "area": "Relativistic stellar equilibrium", "topic": "Physics", "year": 1939, "lane": "HUMAN", "result": "THEORY", "package_id": "oppenheimer-volkoff-ideal-neutron-equilibrium-1939", "target": { "record_id": "urn:uuid:b01e054f-9010-4af4-acf2-5a73906e98ec", "version": 1, "content_hash": "sha256:7676c9f53afcab4b10a641b00506d8899f9ec4103ec1f6ef8ca16e454a260bd2" }, "humans": [ "J. R. Oppenheimer", "G. M. Volkoff" ], "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": [ "chandrasekhar-white-dwarf-limit" ], "subresults": [], "scientific_assessment": { "source_review": "SOURCE_CURATED", "scientific_review": "NOT_REVIEWED_BY_WRS", "formal_replay": "NOT_RUN", "provider_attestation": "NONE" }, "sources": [ { "id": "wrs24-oppenheimer-volkoff-neutron-1939-original", "title": "J. R. Oppenheimer and G. M. Volkoff, On Massive Neutron Cores (Physical Review 55,374-381,15 February1939), original public scan", "url": "https://the-center-of-gravity.com/documents/141/Oppenheimer-Volkoff_On-Massive-Neutron-Cores.pdf" }, { "id": "wrs24-tolman-static-1939-publisher-metadata", "title": "Richard C. Tolman, Static Solutions of Einstein’s Field Equations for Spheres of Fluid (Physical Review 55,364,15 February1939), publisher abstract", "url": "https://journals.aps.org/pr/abstract/10.1103/PhysRev.55.364" } ], "points": "210000", "published_grade": { "id": "oppenheimer-volkoff-ideal-neutron-equilibrium-1939", "entry_id": "oppenheimer-volkoff-ideal-neutron-equilibrium-1939", "band": "A", "modifier": null, "target": { "record_id": "urn:uuid:b01e054f-9010-4af4-acf2-5a73906e98ec", "version": 1, "content_hash": "sha256:7676c9f53afcab4b10a641b00506d8899f9ec4103ec1f6ef8ca16e454a260bd2" }, "what_changed": "Oppenheimer and Volkoff formulate general-relativistic hydrostatic equilibrium for a static spherical fluid and apply it to an ideal cold neutron gas, finding a model-dependent maximum gravitational mass near 0.7 solar masses.", "scope": "Oppenheimer and Volkoff formulate general-relativistic hydrostatic equilibrium for a static spherical fluid and apply it to an ideal cold neutron gas, finding a model-dependent maximum gravitational mass near 0.7 solar masses. The target is the 1939 static, spherical, isotropic perfect-fluid equilibrium formulation and its cold noninteracting neutron-gas application, with zero cosmological constant. Mass/pressure equations require an equation of state, regular central conditions, a pressure-free boundary and exterior matching. The reported about 0.7-solar-mass limit belongs to this ideal equation of state; it is not a universal bound for real neutron stars. Table I samples give a largest listed 0.71, while some web fractions are misread. Thermal energy and forces between neutrons are neglected in the ideal calculation. The authors explicitly acknowledge uncertain extrapolation above nuclear density and consider repulsive-interaction changes; their expectation that the number is near reality is not adopted. Stability is discussed through schematic free-energy reasoning, not an independently reconstructed general perturbation theorem. Numerical integrations, every table glyph and a global uniqueness argument were not replayed. Static equilibrium limits do not themselves supply a general dynamical collapse solution; the Snyder paper is separate. Tolman and earlier degeneracy theory retain credit.", "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:b01e054f-9010-4af4-acf2-5a73906e98ec", "version": 1, "content_hash": "sha256:7676c9f53afcab4b10a641b00506d8899f9ec4103ec1f6ef8ca16e454a260bd2" }, "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": "J. R. Oppenheimer", "note": "Archive attribution; detailed role assignment remains source-bound", "roles": [ "formulator" ], "source": { "citation": "J. R. Oppenheimer and G. M. Volkoff, On Massive Neutron Cores (Physical Review 55,374-381,15 February1939), original public scan", "url": "https://the-center-of-gravity.com/documents/141/Oppenheimer-Volkoff_On-Massive-Neutron-Cores.pdf" } }, { "attribution_basis": "SOURCE_CITED", "credit": "historical_scientific", "entity_kind": "historical_person", "name": "G. M. Volkoff", "note": "Archive attribution; detailed role assignment remains source-bound", "roles": [ "formulator" ], "source": { "citation": "J. R. Oppenheimer and G. M. Volkoff, On Massive Neutron Cores (Physical Review 55,374-381,15 February1939), original public scan", "url": "https://the-center-of-gravity.com/documents/141/Oppenheimer-Volkoff_On-Massive-Neutron-Cores.pdf" } } ], "evidence": [ { "description": "Bibliographic/stated-result source; not a WRS proof verification", "id": "source-0", "kind": "source_reference", "source": { "citation": "J. R. Oppenheimer and G. M. Volkoff, On Massive Neutron Cores (Physical Review 55,374-381,15 February1939), original public scan", "url": "https://the-center-of-gravity.com/documents/141/Oppenheimer-Volkoff_On-Massive-Neutron-Cores.pdf" } }, { "description": "Bibliographic/stated-result source; not a WRS proof verification", "id": "source-1", "kind": "source_reference", "source": { "citation": "Richard C. Tolman, Static Solutions of Einstein’s Field Equations for Spheres of Fluid (Physical Review 55,364,15 February1939), publisher abstract", "url": "https://journals.aps.org/pr/abstract/10.1103/PhysRev.55.364" } } ], "origin": "HUMAN_LEGACY", "record_profile": "wrs-local-research-notes-0.1", "record_type": "research_note", "rrp_version": "0.1", "scope": { "description": "The target is the 1939 static, spherical, isotropic perfect-fluid equilibrium formulation and its cold noninteracting neutron-gas application, with zero cosmological constant. Mass/pressure equations require an equation of state, regular central conditions, a pressure-free boundary and exterior matching. The reported about 0.7-solar-mass limit belongs to this ideal equation of state; it is not a universal bound for real neutron stars. Table I samples give a largest listed 0.71, while some web fractions are misread. Thermal energy and forces between neutrons are neglected in the ideal calculation. The authors explicitly acknowledge uncertain extrapolation above nuclear density and consider repulsive-interaction changes; their expectation that the number is near reality is not adopted. Stability is discussed through schematic free-energy reasoning, not an independently reconstructed general perturbation theorem. Numerical integrations, every table glyph and a global uniqueness argument were not replayed. Static equilibrium limits do not themselves supply a general dynamical collapse solution; the Snyder paper is separate. Tolman and earlier degeneracy theory retain credit.", "domain": "Relativistic stellar equilibrium" }, "sources": [ { "citation": "J. R. Oppenheimer and G. M. Volkoff, On Massive Neutron Cores (Physical Review 55,374-381,15 February1939), original public scan", "url": "https://the-center-of-gravity.com/documents/141/Oppenheimer-Volkoff_On-Massive-Neutron-Cores.pdf" }, { "citation": "Richard C. Tolman, Static Solutions of Einstein’s Field Equations for Spheres of Fluid (Physical Review 55,364,15 February1939), publisher abstract", "url": "https://journals.aps.org/pr/abstract/10.1103/PhysRev.55.364" } ], "statement": "# Oppenheimer and Volkoff: a relativistic neutron-core equilibrium model\n\nOppenheimer and Volkoff formulate general-relativistic hydrostatic equilibrium for a static spherical fluid and apply it to an ideal cold neutron gas, finding a model-dependent maximum gravitational mass near 0.7 solar masses.\n\nPressure can support a compact star, but pressure and internal energy also affect gravity in relativity. The authors turn that balance into equations for a spherical star and numerically explore a simple cold neutron gas. The resulting sequence reaches a largest supported mass in that model. The reusable contribution is the equilibrium framework and an explicit demonstration that the material law matters; the historical ideal-gas number is not a measurement of every real neutron star.\n\n## Scientific scope\n\nThe target is the 1939 static, spherical, isotropic perfect-fluid equilibrium formulation and its cold noninteracting neutron-gas application, with zero cosmological constant. Mass/pressure equations require an equation of state, regular central conditions, a pressure-free boundary and exterior matching. The reported about 0.7-solar-mass limit belongs to this ideal equation of state; it is not a universal bound for real neutron stars. Table I samples give a largest listed 0.71, while some web fractions are misread. Thermal energy and forces between neutrons are neglected in the ideal calculation. The authors explicitly acknowledge uncertain extrapolation above nuclear density and consider repulsive-interaction changes; their expectation that the number is near reality is not adopted. Stability is discussed through schematic free-energy reasoning, not an independently reconstructed general perturbation theorem. Numerical integrations, every table glyph and a global uniqueness argument were not replayed. Static equilibrium limits do not themselves supply a general dynamical collapse solution; the Snyder paper is separate. Tolman and earlier degeneracy theory retain credit.\n\n## People and systems\n\nJ. R. Oppenheimer; G. M. Volkoff\n\n\n\n## Original sources\n\n- [J. R. Oppenheimer and G. M. Volkoff, On Massive Neutron Cores (Physical Review 55,374-381,15 February1939), original public scan](https://the-center-of-gravity.com/documents/141/Oppenheimer-Volkoff_On-Massive-Neutron-Cores.pdf)\n- [Richard C. Tolman, Static Solutions of Einstein’s Field Equations for Spheres of Fluid (Physical Review 55,364,15 February1939), publisher abstract](https://journals.aps.org/pr/abstract/10.1103/PhysRev.55.364)\n", "summary": "Oppenheimer and Volkoff formulate general-relativistic hydrostatic equilibrium for a static spherical fluid and apply it to an ideal cold neutron gas, finding a model-dependent maximum gravitational mass near 0.7 solar masses.\n\nPressure can support a compact star, but pressure and internal energy also affect gravity in relativity. The authors turn that balance into equations for a spherical star and numerically explore a simple cold neutron gas. The resulting sequence reaches a largest supported mass in that model. The reusable contribution is the equilibrium framework and an explicit demonstration that the material law matters; the historical ideal-gas number is not a measurement of every real neutron star.", "title": "Oppenheimer and Volkoff: a relativistic neutron-core equilibrium model" }, "record_id": "urn:uuid:b01e054f-9010-4af4-acf2-5a73906e98ec", "version": 1, "source_ref": { "record_id": "urn:uuid:b01e054f-9010-4af4-acf2-5a73906e98ec", "version": 1, "content_hash": "sha256:7676c9f53afcab4b10a641b00506d8899f9ec4103ec1f6ef8ca16e454a260bd2" }, "export_view": "wrs-public-editorial-view-1", "public_view_hash": "sha256:7ffa67a9c4aa7f89a81786f053f42901f1c24534c505b12e655cb2564897e3dd" }, "target": { "record_id": "urn:uuid:b01e054f-9010-4af4-acf2-5a73906e98ec", "version": 1, "content_hash": "sha256:7676c9f53afcab4b10a641b00506d8899f9ec4103ec1f6ef8ca16e454a260bd2" }, "published_grade": { "profile": "wrs-published-grade-1", "edition": "2026-10-28.1", "id": "oppenheimer-volkoff-ideal-neutron-equilibrium-1939", "entry_id": "oppenheimer-volkoff-ideal-neutron-equilibrium-1939", "revision": 1, "title": "Oppenheimer and Volkoff: a relativistic neutron-core equilibrium model", "context": "Relativistic stellar equilibrium", "track": "Relativistic stellar equilibrium", "band": "A", "modifier": null, "status": "PROVISIONAL_EDITORIAL", "assessed_on": "2026-10-04", "evidence_cutoff": "2026-10-04", "achievement_state": "SUPPORTED_SCOPED_RESULT", "what_changed": "Oppenheimer and Volkoff formulate general-relativistic hydrostatic equilibrium for a static spherical fluid and apply it to an ideal cold neutron gas, finding a model-dependent maximum gravitational mass near 0.7 solar masses.", "scope": "Oppenheimer and Volkoff formulate general-relativistic hydrostatic equilibrium for a static spherical fluid and apply it to an ideal cold neutron gas, finding a model-dependent maximum gravitational mass near 0.7 solar masses. The target is the 1939 static, spherical, isotropic perfect-fluid equilibrium formulation and its cold noninteracting neutron-gas application, with zero cosmological constant. Mass/pressure equations require an equation of state, regular central conditions, a pressure-free boundary and exterior matching. The reported about 0.7-solar-mass limit belongs to this ideal equation of state; it is not a universal bound for real neutron stars. Table I samples give a largest listed 0.71, while some web fractions are misread. Thermal energy and forces between neutrons are neglected in the ideal calculation. The authors explicitly acknowledge uncertain extrapolation above nuclear density and consider repulsive-interaction changes; their expectation that the number is near reality is not adopted. Stability is discussed through schematic free-energy reasoning, not an independently reconstructed general perturbation theorem. Numerical integrations, every table glyph and a global uniqueness argument were not replayed. Static equilibrium limits do not themselves supply a general dynamical collapse solution; the Snyder paper is separate. Tolman and earlier degeneracy theory retain credit.", "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": "J. R. Oppenheimer and G. M. Volkoff, On Massive Neutron Cores (Physical Review 55,374-381,15 February 1939), original public scan", "url": "https://the-center-of-gravity.com/documents/141/Oppenheimer-Volkoff_On-Massive-Neutron-Cores.pdf", "locator": "Original linked work. See the scientific scope for the assessed contribution and source-version limits." }, { "title": "Richard C. Tolman, Static Solutions of Einstein’s Field Equations for Spheres of Fluid (Physical Review 55,364,15 February 1939), publisher abstract", "url": "https://journals.aps.org/pr/abstract/10.1103/PhysRev.55.364", "locator": "Original linked work. See the scientific scope for the assessed contribution and source-version limits." } ], "roles": [ { "who": "J. R. Oppenheimer", "did": "Original source-listed scientific author of this scoped work; byline does not determine effort fractions.", "credit": "SCIENCE" }, { "who": "G. M. 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