stress–energy tensor
E378339
energy–momentum tensor
object in general relativity
object in special relativity
physical quantity
rank-2 tensor
tensor
The stress–energy tensor is a fundamental object in relativity that encodes the density and flow of energy and momentum in spacetime, acting as the source term for gravitational and electromagnetic field equations.
All labels observed (2)
| Label | Occurrences |
|---|---|
| energy-momentum tensor | 1 |
| stress–energy tensor canonical | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T3676898 — 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: stress–energy tensor Context triple: [Einstein–Maxwell equations, uses, stress–energy 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.
-
B.
Maxwell stress tensor
The Maxwell stress tensor is a mathematical construct in classical electromagnetism that represents how electric and magnetic fields transmit mechanical stresses, such as pressure and tension, through space and matter.
-
C.
Weyl tensor
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.
-
D.
Ricci-Curbastro
Ricci-Curbastro is the surname of the Italian mathematician Gregorio Ricci-Curbastro, a pioneer of tensor calculus and differential geometry.
-
E.
Cauchy stress tensor
The Cauchy stress tensor is a fundamental concept in continuum mechanics that mathematically represents the internal distribution of forces (stresses) within a deformable material at a point.
- 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: stress–energy tensor Target entity description: The stress–energy tensor is a fundamental object in relativity that encodes the density and flow of energy and momentum in spacetime, acting as the source term for gravitational and electromagnetic field equations.
-
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.
Maxwell stress tensor
The Maxwell stress tensor is a mathematical construct in classical electromagnetism that represents how electric and magnetic fields transmit mechanical stresses, such as pressure and tension, through space and matter.
-
C.
Weyl tensor
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.
-
D.
Ricci-Curbastro
Ricci-Curbastro is the surname of the Italian mathematician Gregorio Ricci-Curbastro, a pioneer of tensor calculus and differential geometry.
-
E.
Cauchy stress tensor
The Cauchy stress tensor is a fundamental concept in continuum mechanics that mathematically represents the internal distribution of forces (stresses) within a deformable material at a point.
- F. None of above. chosen
Statements (50)
| Predicate | Object |
|---|---|
| instanceOf |
energy–momentum tensor
ⓘ
object in general relativity ⓘ object in special relativity ⓘ physical quantity ⓘ rank-2 tensor ⓘ tensor ⓘ |
| alsoKnownAs |
energy–momentum tensor
ⓘ
stress–energy–momentum tensor ⓘ |
| appearsInEquation |
Einstein field equations
ⓘ
conservation of energy–momentum equations ⓘ |
| componentIndexType | spacetime indices ⓘ |
| componentType |
T_{00}
ⓘ
T_{0i} ⓘ T_{i0} ⓘ T_{ij} ⓘ |
| covariantConservationLaw | ∇_μ T^{μν} = 0 ⓘ |
| definedOn | four-dimensional spacetime manifold ⓘ |
| dependsOn | metric tensor ⓘ |
| domain | spacetime ⓘ |
| electromagneticFieldForm | T^{μν} = F^{μα} F^{ν}{}_{α} - 1/4 g^{μν} F_{αβ} F^{αβ} ⓘ |
| encodes |
energy density
ⓘ
energy flux ⓘ momentum density ⓘ momentum flux ⓘ pressure ⓘ shear stress ⓘ |
| frameDependence | components depend on observer 4-velocity ⓘ |
| governs |
flow of energy in spacetime
ⓘ
flow of momentum in spacetime ⓘ |
| hasFormFor |
dust
ⓘ
electromagnetic field ⓘ perfect fluid ⓘ scalar field ⓘ |
| mathematicalProperty | covariantly conserved ⓘ |
| perfectFluidForm | T^{μν} = (ρ + p) u^{μ} u^{ν} + p g^{μν} ⓘ |
| relatedTo |
Noether's theorem
ⓘ
surface form:
Noether theorem
spacetime translation invariance ⓘ |
| roleInTheory |
source of spacetime curvature
ⓘ
source term in Einstein field equations ⓘ source term in relativistic field equations ⓘ |
| satisfies | local conservation of energy–momentum ⓘ |
| symbol | T_{\ ⓘ |
| T_{00}Represents | energy density ⓘ |
| T_{0i}Represents | energy flux ⓘ |
| T_{i0}Represents | momentum density ⓘ |
| T_{ij}Represents | stress components ⓘ |
| usedIn |
cosmology
ⓘ
field theory in curved spacetime ⓘ general relativistic magnetohydrodynamics ⓘ relativistic hydrodynamics ⓘ |
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: stress–energy tensor Description of subject: The stress–energy tensor is a fundamental object in relativity that encodes the density and flow of energy and momentum in spacetime, acting as the source term for gravitational and electromagnetic field equations.
Referenced by (2)
Full triples — surface form annotated when it differs from this entity's canonical label.
this entity surface form:
energy-momentum tensor