Einstein–Yang–Mills equations
E378340
The Einstein–Yang–Mills equations are the coupled field equations that describe how non-abelian gauge fields (such as those in Yang–Mills theory) interact with and curve spacetime within the framework of general relativity.
All labels observed (2)
| Label | Occurrences |
|---|---|
| Einstein–Yang–Mills equations canonical | 1 |
| Einstein–Yang–Mills–Higgs equations | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T3676922 — 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: Einstein–Yang–Mills equations Context triple: [Einstein–Maxwell equations, relatedTo, Einstein–Yang–Mills equations]
-
A.
Einstein–Maxwell equations
The Einstein–Maxwell equations are the coupled set of field equations in general relativity that describe how spacetime curvature and electromagnetic fields interact and influence each other.
-
B.
Yang–Mills theory
Yang–Mills theory is a gauge field theory describing the behavior of non-abelian gauge fields, forming the mathematical foundation for modern particle physics, including the strong and electroweak interactions.
-
C.
Landau–Lifshitz equations
The Landau–Lifshitz equations are fundamental differential equations in theoretical physics that describe the dynamics of magnetization in ferromagnets and, more broadly, the behavior of fields in relativistic and nonrelativistic continuum theories.
-
D.
Weyl’s gauge theory
Weyl’s gauge theory is an early 20th-century theoretical framework that introduced the concept of local gauge invariance, laying foundational ideas for modern gauge theories in particle physics.
-
E.
Einstein field equations
The Einstein field equations are the core mathematical framework of general relativity, relating the curvature of spacetime to the distribution of matter and energy.
- 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: Einstein–Yang–Mills equations Target entity description: The Einstein–Yang–Mills equations are the coupled field equations that describe how non-abelian gauge fields (such as those in Yang–Mills theory) interact with and curve spacetime within the framework of general relativity.
-
A.
Einstein–Maxwell equations
The Einstein–Maxwell equations are the coupled set of field equations in general relativity that describe how spacetime curvature and electromagnetic fields interact and influence each other.
-
B.
Yang–Mills theory
Yang–Mills theory is a gauge field theory describing the behavior of non-abelian gauge fields, forming the mathematical foundation for modern particle physics, including the strong and electroweak interactions.
-
C.
Landau–Lifshitz equations
The Landau–Lifshitz equations are fundamental differential equations in theoretical physics that describe the dynamics of magnetization in ferromagnets and, more broadly, the behavior of fields in relativistic and nonrelativistic continuum theories.
-
D.
Weyl’s gauge theory
Weyl’s gauge theory is an early 20th-century theoretical framework that introduced the concept of local gauge invariance, laying foundational ideas for modern gauge theories in particle physics.
-
E.
Einstein field equations
The Einstein field equations are the core mathematical framework of general relativity, relating the curvature of spacetime to the distribution of matter and energy.
- F. None of above. chosen
Statements (47)
| Predicate | Object |
|---|---|
| instanceOf |
gauge field equations
ⓘ
gravitational field equations ⓘ system of coupled field equations ⓘ |
| aimsToModel | coupling of fundamental gauge interactions to gravity ⓘ |
| appliesTo | non-abelian gauge fields in curved spacetime ⓘ |
| assumes |
Lorentzian spacetime manifold
ⓘ
principal fiber bundle with compact gauge group ⓘ |
| basedOn |
Einstein field equations
ⓘ
Yang–Mills theory ⓘ
surface form:
Yang–Mills equations
|
| describes |
backreaction of gauge fields on spacetime geometry
ⓘ
curvature of spacetime sourced by Yang–Mills fields ⓘ interaction between non-abelian gauge fields and gravity ⓘ |
| domain | classical field theory ⓘ |
| fieldOfStudy |
gauge theory
ⓘ
general relativity ⓘ mathematical physics ⓘ theoretical physics ⓘ |
| generalizes |
Einstein–Maxwell equations
ⓘ
Yang–Mills theory ⓘ
surface form:
flat-space Yang–Mills equations
Einstein field equations ⓘ
surface form:
vacuum Einstein equations
|
| hasMathematicalForm |
D_{μ} F^{a μν} = 0 in curved spacetime
ⓘ
G_{μν} = 8πG T^{YM}_{μν} ⓘ |
| hasPart |
Einstein equations with Yang–Mills stress–energy tensor
ⓘ
Yang–Mills equations on a curved spacetime background ⓘ |
| involves |
Bianchi identities
ⓘ
Einstein–Hilbert action ⓘ
surface form:
Einstein–Hilbert action with Yang–Mills term
conservation of stress–energy ⓘ gauge group SU(N) ⓘ variation of an action functional ⓘ |
| mathematicalStructure |
nonlinear partial differential equations
ⓘ
tensor equations on a manifold ⓘ |
| relatedTo |
Einstein–Yang–Mills equations
self-linksurface differs
ⓘ
surface form:
Einstein–Yang–Mills–Higgs equations
Kaluza–Klein theory ⓘ
surface form:
Kaluza–Klein theories
unified field theories ⓘ |
| symmetry |
diffeomorphism invariance
ⓘ
local gauge invariance ⓘ |
| usedIn |
cosmological models with gauge fields
ⓘ
high-energy astrophysics models ⓘ studies of black holes with non-abelian hair ⓘ studies of classical gauge field solitons coupled to gravity ⓘ |
| usesConcept |
covariant derivative
ⓘ
field strength tensor ⓘ gauge connection ⓘ non-abelian gauge field ⓘ spacetime metric ⓘ stress–energy tensor ⓘ |
| validInRegime | classical, non-quantum description of fields ⓘ |
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: Einstein–Yang–Mills equations Description of subject: The Einstein–Yang–Mills equations are the coupled field equations that describe how non-abelian gauge fields (such as those in Yang–Mills theory) interact with and curve spacetime within the framework of general relativity.
Referenced by (2)
Full triples — surface form annotated when it differs from this entity's canonical label.
Einstein–Yang–Mills equations
→
relatedTo
→
Einstein–Yang–Mills equations
self-linksurface differs
ⓘ
this entity surface form:
Einstein–Yang–Mills–Higgs equations