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.

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All labels observed (3)

Label	Occurrences
Rosenfeld stress–energy tensor	1
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 theorem ⓘ linked to: Noether's 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

Referenced by (3)

Full triples — surface form annotated when it differs from this entity's canonical label.

Einstein–Maxwell equations → uses → stress–energy tensor ⓘ

graviton (hypothetical) → couplesTo → energy-momentum tensor ⓘ

linked to: stress–energy tensor

Léon Rosenfeld → notableWork → Rosenfeld stress–energy tensor ⓘ