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 (2)

Label	Occurrences
energy-momentum tensor	1
stress–energy tensor canonical	1

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.

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

graviton (hypothetical) → couplesTo → stress–energy tensor ⓘ

this entity surface form: energy-momentum tensor