Einstein field equations

E1603

equations of general relativity fundamental physical law system of equations tensor equation

The Einstein field equations are the core mathematical framework of general relativity, relating the curvature of spacetime to the distribution of matter and energy.

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Observed surface forms (4)

Surface form	Occurrences
Friedmann equations	2
Einstein equations	1
Einstein field equations (via κ = 8πG/c^4)	1
Einstein field equations formulation	1

Statements (49)

Predicate	Object
instanceOf	equations of general relativity ⓘ fundamental physical law ⓘ system of equations ⓘ tensor equation ⓘ
admitsSolution	FLRW cosmological models ⓘ surface form: Friedmann–Lemaître–Robertson–Walker metric Kerr metric ⓘ Minkowski space-time ⓘ surface form: Minkowski spacetime Reissner–Nordström metric ⓘ Schwarzschild black hole ⓘ surface form: Schwarzschild metric de Sitter spacetime ⓘ
basedOnPrinciple	equivalence principle ⓘ general covariance ⓘ
constant	Newtonian gravitational constant G ⓘ cosmological constant \Lambda ⓘ speed of light c ⓘ
contrastsWith	quantum gravity theories ⓘ
describes	relationship between spacetime curvature and energy-momentum ⓘ
difficulty	analytical solutions are rare ⓘ
domain	classical gravitation ⓘ
field	general relativity ⓘ
foundationOf	modern cosmology ⓘ
hasVacuumForm	G_{\mu\nu} + \Lambda g_{\mu\nu} = 0 ⓘ R_{\mu\nu} = 0 (for \Lambda = 0 and vacuum) ⓘ
includes	cosmological constant ⓘ
introducedBy	Albert Einstein ⓘ
invariantUnder	general coordinate transformations ⓘ
numberOfIndependentEquations	10 ⓘ
order	second-order partial differential equations ⓘ
predicts	black holes ⓘ gravitational lensing ⓘ gravitational time dilation ⓘ gravitational waves ⓘ
publishedIn	Annalen der Physik ⓘ
reducesTo	Newtonian gravity in the weak-field limit ⓘ
relates	geometry of spacetime to matter and energy ⓘ
spacetimeDimensionAssumed	4 ⓘ
symbolicallyWrittenAs	G_{\mu\nu} + \Lambda g_{\mu\nu} = \frac{8\pi G}{c^4} T_{\mu\nu} ⓘ
tensorRank	2 ⓘ
type	nonlinear equations ⓘ
usedIn	astrophysics ⓘ cosmological models ⓘ gravitational wave modeling ⓘ numerical relativity ⓘ
uses	Einstein tensor ⓘ Ricci curvature tensor ⓘ Ricci scalar ⓘ metric tensor ⓘ stress–energy tensor ⓘ
yearProposed	1915 ⓘ

Referenced by (24)

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

Ricci curvature tensor → appearsIn → Einstein field equations ⓘ

Ricci scalar → appearsIn → Einstein field equations ⓘ

Einstein tensor → appearsInEquation → Einstein field equations ⓘ

Newtonian gravitational constant G → appearsInEquation → Einstein field equations ⓘ

this entity surface form: Einstein field equations (via κ = 8πG/c^4)

black hole no-hair theorem → assumes → Einstein field equations ⓘ

Einstein–Maxwell equations → basedOn → Einstein field equations ⓘ

Oppenheimer–Volkoff limit → basedOn → Einstein field equations ⓘ

Schwarzschild Penrose diagram → basedOn → Einstein field equations ⓘ

Einstein–Rosen bridge → basedOnSolutionOf → Einstein field equations ⓘ

On the Curvature of Space → basedOnTheory → Einstein field equations ⓘ

theory of relativity → coreConcept → Einstein field equations ⓘ

general relativity → coreEquation → Einstein field equations ⓘ

FLRW cosmological models → governedBy → Einstein field equations ⓘ

this entity surface form: Friedmann equations

Arthur Geoffrey Walker → hasResearchInterest → Einstein field equations ⓘ

Die Grundlage der allgemeinen Relativitätstheorie → introduces → Einstein field equations ⓘ

Israel–Carter–Robinson uniqueness theorems → involves → Einstein field equations ⓘ

Albert Einstein → knownFor → Einstein field equations ⓘ

The Mathematical Theory of Black Holes → mainSubject → Einstein field equations ⓘ

Lorentzian geometry → providesFrameworkFor → Einstein field equations ⓘ

Einstein–Maxwell equations → relatedTo → Einstein field equations ⓘ

this entity surface form: Einstein equations

On the Curvature of Space → relatedTo → Einstein field equations ⓘ

this entity surface form: Friedmann equations

"Über das Gravitationsfeld eines Massenpunktes nach der Einsteinschen Theorie" → topic → Einstein field equations ⓘ

subject surface form: Über das Gravitationsfeld eines Massenpunktes nach der Einsteinschen Theorie

Christoffel symbols → usedIn → Einstein field equations ⓘ

this entity surface form: Einstein field equations formulation

Riemann curvature tensor → usedIn → Einstein field equations ⓘ