On the Curvature of Space
E87936
"On the Curvature of Space" is a pioneering 1922 paper by Alexander Friedmann that introduced non-static, expanding-universe solutions to Einstein’s field equations, laying the theoretical foundation for modern cosmology.
All labels observed (2)
| Label | Occurrences |
|---|---|
| On the Curvature of Space canonical | 1 |
| On the Possibility of a World with Constant Negative Curvature of Space | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T744293 — resolving that mention is where its identity was fixed. The disambiguator weighed these candidate entities and picked the highlighted one (or “None”, minting a new entity). This is how homonymy is resolved: the same surface form can point to different entities.
Target entity: On the Curvature of Space Context triple: [Alexander Friedmann, notableWork, On the Curvature of Space]
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A.
The Mathematical Theory of Black Holes
The Mathematical Theory of Black Holes is a landmark monograph that presents a rigorous, comprehensive treatment of the physics and mathematics underlying black hole solutions in general relativity.
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B.
Time And Relative Dimension In Space
Time And Relative Dimension In Space is the full name of the Doctor Who franchise’s iconic time-traveling spacecraft and time machine, commonly known by its acronym TARDIS.
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C.
Schwarzschild–Milne equations
The Schwarzschild–Milne equations are fundamental integro-differential equations in radiative transfer theory that describe the propagation and scattering of radiation through a plane-parallel, absorbing and emitting medium.
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D.
Theorema Egregium
Theorema Egregium is Gauss’s celebrated theorem in differential geometry showing that the Gaussian curvature of a surface is an intrinsic property independent of how the surface is embedded in space.
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E.
Does the Inertia of a Body Depend Upon Its Energy Content?
"Does the Inertia of a Body Depend Upon Its Energy Content?" is Albert Einstein’s 1905 paper that first articulated the mass–energy equivalence principle, commonly expressed as E = mc².
- F. None of above. chosen
- G. Unsure - the case is ambiguous/there is not enough information to decide.
Target entity: On the Curvature of Space Target entity description: "On the Curvature of Space" is a pioneering 1922 paper by Alexander Friedmann that introduced non-static, expanding-universe solutions to Einstein’s field equations, laying the theoretical foundation for modern cosmology.
-
A.
The Mathematical Theory of Black Holes
The Mathematical Theory of Black Holes is a landmark monograph that presents a rigorous, comprehensive treatment of the physics and mathematics underlying black hole solutions in general relativity.
-
B.
Time And Relative Dimension In Space
Time And Relative Dimension In Space is the full name of the Doctor Who franchise’s iconic time-traveling spacecraft and time machine, commonly known by its acronym TARDIS.
-
C.
Schwarzschild–Milne equations
The Schwarzschild–Milne equations are fundamental integro-differential equations in radiative transfer theory that describe the propagation and scattering of radiation through a plane-parallel, absorbing and emitting medium.
-
D.
Theorema Egregium
Theorema Egregium is Gauss’s celebrated theorem in differential geometry showing that the Gaussian curvature of a surface is an intrinsic property independent of how the surface is embedded in space.
-
E.
Does the Inertia of a Body Depend Upon Its Energy Content?
"Does the Inertia of a Body Depend Upon Its Energy Content?" is Albert Einstein’s 1905 paper that first articulated the mass–energy equivalence principle, commonly expressed as E = mc².
- F. None of above. chosen
Statements (47)
| Predicate | Object |
|---|---|
| instanceOf |
cosmology paper
ⓘ
physics paper ⓘ scientific paper ⓘ |
| acknowledgedBy | 20th-century cosmologists ⓘ |
| assumes |
homogeneity of the universe
ⓘ
isotropy of the universe ⓘ |
| author | Alexander Friedmann ⓘ |
| basedOnTheory | Einstein field equations ⓘ |
| contribution |
demonstrated possibility of expanding universe
ⓘ
provided mathematical basis for homogeneous and isotropic cosmological models ⓘ showed that Einstein field equations admit time-dependent solutions ⓘ |
| countryOfOrigin |
Soviet Union
ⓘ
surface form:
Soviet Russia
|
| criticizedBy | Albert Einstein ⓘ |
| describes |
closed universe models
ⓘ
negatively curved space ⓘ open universe models ⓘ positively curved space ⓘ spatially homogeneous universes ⓘ |
| field |
cosmology
ⓘ
theoretical physics ⓘ |
| historicalSignificance |
first publication of expanding-universe solutions
ⓘ
foundation for relativistic cosmology ⓘ |
| influenced |
Big Bang
ⓘ
surface form:
Big Bang theory
Georges Lemaître's cosmological work ⓘ modern cosmology ⓘ |
| influencedBy | Albert Einstein's theory of general relativity ⓘ |
| introducedConcept |
expanding universe solutions
ⓘ
non-static cosmological solutions ⓘ |
| language | Russian ⓘ |
| laterRecognizedAs | pioneering work in cosmology ⓘ |
| mathematicalTool |
Riemannian geometry
ⓘ
differential equations ⓘ |
| proposedModel |
FLRW cosmological models
ⓘ
surface form:
Friedmann cosmological models
FLRW cosmological models ⓘ
surface form:
Friedmann–Lemaître–Robertson–Walker metric
|
| publicationYear | 1922 ⓘ |
| relatedTo |
Einstein static universe
ⓘ
Einstein field equations ⓘ
surface form:
Friedmann equations
cosmological constant ⓘ |
| status | landmark paper in cosmology ⓘ |
| timeDependence | scale factor of the universe ⓘ |
| topic |
cosmic expansion
ⓘ
curvature of space ⓘ dynamics of the universe ⓘ non-static universe ⓘ |
| usesConcept |
cosmological principle
ⓘ
curved spacetime ⓘ general relativity ⓘ |
How these facts were elicited
The pipeline generated the facts above by prompting gpt-5.1 with this entity's name + description and the instruction below.
You are a knowledge base construction expert. Given a subject entity and a description of it, return factual statements that you know for the subject as a JSON list of dictionaries(triples), where keys must be "subject", "predicate" and "object". The number of facts may be very high, between 25 to 50 or more, for very popular subjects. For less popular subjects, the number of facts can be very low, like 5 or 10. # Requirements - If you don't know the subject at all, return an empty list. - If the subject is not a named entity, return an empty list. - Include at least one triple where predicate is "instanceOf". - Do not get too wordy. - Separate several objects into multiple triples with one object.
Subject: On the Curvature of Space Description of subject: "On the Curvature of Space" is a pioneering 1922 paper by Alexander Friedmann that introduced non-static, expanding-universe solutions to Einstein’s field equations, laying the theoretical foundation for modern cosmology.
Referenced by (2)
Full triples — surface form annotated when it differs from this entity's canonical label.