Weyl tensor
E287410
The Weyl tensor is the traceless part of the Riemann curvature tensor in differential geometry and general relativity, encoding the purely shape-distorting (conformal) aspects of spacetime curvature independent of matter content.
All labels observed (2)
| Label | Occurrences |
|---|---|
| Weyl tensor canonical | 2 |
| conformal curvature tensor | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T2683225 — 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.
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Weyl tensor Context triple: [Ricci scalar, relatedTo, Weyl tensor]
-
A.
Einstein tensor
The Einstein tensor is a mathematical object in general relativity that encapsulates how spacetime curvature is related to the distribution of matter and energy.
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B.
Riemann curvature tensor
The Riemann curvature tensor is a fundamental geometric object in differential geometry that measures how much a Riemannian manifold deviates from being flat by encoding the intrinsic curvature of the space.
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C.
Ricci-Curbastro
Ricci-Curbastro is the surname of the Italian mathematician Gregorio Ricci-Curbastro, a pioneer of tensor calculus and differential geometry.
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D.
Ricci curvature tensor
The Ricci curvature tensor is a geometric object in differential geometry that measures how volumes in a curved space-time deviate from those in flat space, playing a central role in general relativity.
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E.
Kretschmann scalar
The Kretschmann scalar is a curvature invariant in general relativity that combines components of the Riemann tensor into a single scalar quantity used to characterize the intensity of spacetime curvature, especially near singularities.
- F. None of above. chosen
- G. Unsure - the case is ambiguous/there is not enough information to decide.
NED2
Entity disambiguation (via description)
gpt-5-mini-2025-08-07
Target entity: Weyl tensor Target entity description: The Weyl tensor is the traceless part of the Riemann curvature tensor in differential geometry and general relativity, encoding the purely shape-distorting (conformal) aspects of spacetime curvature independent of matter content.
-
A.
Einstein tensor
The Einstein tensor is a mathematical object in general relativity that encapsulates how spacetime curvature is related to the distribution of matter and energy.
-
B.
Riemann curvature tensor
The Riemann curvature tensor is a fundamental geometric object in differential geometry that measures how much a Riemannian manifold deviates from being flat by encoding the intrinsic curvature of the space.
-
C.
Ricci-Curbastro
Ricci-Curbastro is the surname of the Italian mathematician Gregorio Ricci-Curbastro, a pioneer of tensor calculus and differential geometry.
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D.
Ricci curvature tensor
The Ricci curvature tensor is a geometric object in differential geometry that measures how volumes in a curved space-time deviate from those in flat space, playing a central role in general relativity.
-
E.
Kretschmann scalar
The Kretschmann scalar is a curvature invariant in general relativity that combines components of the Riemann tensor into a single scalar quantity used to characterize the intensity of spacetime curvature, especially near singularities.
- F. None of above. chosen
Statements (48)
| Predicate | Object |
|---|---|
| instanceOf |
curvature tensor
ⓘ
geometric object ⓘ mathematical tensor ⓘ |
| alsoKnownAs |
Weyl tensor
ⓘ
surface form:
conformal curvature tensor
|
| appearsIn | Petrov classification ⓘ |
| canBeNonzeroIn | vacuum regions of spacetime ⓘ |
| captures | nonlocal aspects of gravitational field ⓘ |
| decomposition | Riemann = Weyl + Ricci-part + scalar-curvature-part ⓘ |
| definedOn |
Riemannian manifold
ⓘ
pseudo-Riemannian manifold ⓘ |
| describes |
free gravitational field
ⓘ
tidal gravitational effects in vacuum ⓘ |
| dimensionRequirement | manifold dimension ≥ 3 ⓘ |
| doesNotDependOn | local matter content ⓘ |
| encodes |
conformal curvature
ⓘ
shape-distorting aspects of curvature ⓘ |
| field |
differential geometry
ⓘ
general relativity ⓘ |
| hasSymmetry |
antisymmetric in first and second index pairs
ⓘ
satisfies first Bianchi identity ⓘ symmetric under exchange of index pairs ⓘ |
| isComponentOf | spacetime curvature ⓘ |
| isConformallyInvariant | in dimension 4 ⓘ |
| isConstructedFrom |
Ricci tensor
ⓘ
Riemann curvature tensor ⓘ
surface form:
Riemann tensor
scalar curvature ⓘ |
| isDivergenceFreeIn | vacuum Einstein equations ⓘ |
| isIndependentOf | Ricci tensor ⓘ |
| isPartOf |
Riemann curvature tensor
ⓘ
surface form:
Riemann curvature tensor decomposition
|
| isTraceless | with respect to any pair of indices ⓘ |
| isTracelessPartOf | Riemann curvature tensor ⓘ |
| isUsedIn |
conformal geometry
ⓘ
mathematical relativity ⓘ study of gravitational waves ⓘ |
| isUsedToDefine |
Newman–Penrose formalism
ⓘ
surface form:
Newman–Penrose Weyl scalars
|
| isZeroIfAndOnlyIf | spacetime is locally conformally flat (dimension ≥ 4) ⓘ |
| isZeroIn |
Minkowski space-time
ⓘ
surface form:
Minkowski spacetime
|
| namedAfter | Hermann Weyl ⓘ |
| rank |
(0,4) tensor
ⓘ
(1,3) tensor ⓘ |
| relatedTo | gravitational radiation ⓘ |
| satisfies |
Bianchi identities
ⓘ
same index symmetries as Riemann tensor ⓘ |
| transformsHomogeneouslyUnder | conformal rescalings of the metric ⓘ |
| usedFor | classifying algebraic types of spacetime curvature ⓘ |
| vanishesIdenticallyIn |
all 2-dimensional manifolds
ⓘ
all conformally flat manifolds ⓘ |
| vanishesIn |
FLRW cosmological models
ⓘ
surface form:
Friedmann–Lemaître–Robertson–Walker spacetimes
|
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.
Instruction
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.
Input
Subject: Weyl tensor Description of subject: The Weyl tensor is the traceless part of the Riemann curvature tensor in differential geometry and general relativity, encoding the purely shape-distorting (conformal) aspects of spacetime curvature independent of matter content.
Referenced by (3)
Full triples — surface form annotated when it differs from this entity's canonical label.
this entity surface form:
conformal curvature tensor