Einstein tensor
E7353
The Einstein tensor is a mathematical object in general relativity that encapsulates how spacetime curvature is related to the distribution of matter and energy.
Statements (48)
| Predicate | Object |
|---|---|
| instanceOf |
geometric object
→
object in general relativity → rank-2 tensor → tensor field → |
| appearsInEquation |
Einstein field equations
→
|
| constructedFrom |
Ricci scalar
→
Ricci tensor → metric tensor → |
| coordinateIndependence |
tensorial
→
|
| definedInTermsOf |
Riemann curvature tensor via contractions
→
|
| definedOn |
spacetime manifold
→
|
| dependsOn |
Christoffel symbols
→
Levi-Civita connection → |
| derivedFrom |
contracted Bianchi identities
→
|
| domain |
four-dimensional Lorentzian manifolds
→
|
| encodes |
curvature information relevant to gravitation
→
|
| equatedTo |
stress-energy tensor up to constants
→
|
| equation |
G_{\mu\nu} = R_{\mu\nu} - \tfrac{1}{2} R g_{\mu\nu}
→
|
| equationContext |
G_{\mu\nu} = 8\pi G T_{\mu\nu} / c^{4}
→
|
| field |
differential geometry
→
gravitational physics → mathematical physics → |
| hasDivergence |
zero
→
|
| hasSymbol |
G_{\mu\nu}
→
G_{ab} → |
| indexStructure |
two covariant indices
→
|
| introducedBy |
Albert Einstein
→
|
| isSymmetric |
true
→
|
| livesIn |
tangent bundle
→
|
| property |
covariantly divergence-free
→
|
| rank |
2
→
|
| relatedConcept |
Bianchi identities
→
Ricci scalar → Ricci tensor → metric tensor → stress-energy tensor → |
| relatesTo |
distribution of energy
→
distribution of matter → spacetime curvature → |
| roleInPhysics |
acts as geometric side of Einstein field equations
→
|
| satisfiesIdentity |
\nabla_{\mu} G^{\mu}{}_{\nu} = 0
→
|
| symmetryProperty |
G_{\mu\nu} = G_{\nu\mu}
→
|
| transformationProperty |
transforms as a (0,2) tensor under coordinate changes
→
|
| type |
(0,2) tensor
→
|
| usedFor |
describing gravitational field
→
formulating gravitational dynamics → |
| usedInTheory |
general relativity
→
|
| vanishesWhen |
spacetime is Ricci-flat
→
|
Referenced by (4)
| Subject (surface form when different) | Predicate |
|---|---|
|
Einstein field equations
→
Einstein–Maxwell equations → |
uses |
|
Ricci curvature tensor
→
|
relatedTo |
|
Bianchi identities
→
|
relatesTo |