Einstein tensor Guide, Meaning , Facts, Information and Description
In
differential geometry, the
Einstein tensor is a 2-tensor defined over Riemannian manifolds, which, in components, is expressed as
- ,
where is the
Ricci tensor, is the
metric of the manifold, and is the
scalar curvature. The
Bianchi identities can be easily expressed with the aid of the Einstein tensor:
- .
In
general relativity, the Einstein tensor allows a compact expression of the Einstein equations:
- .
The Bianchi identities automatically ensure the conservation of the
energy-momentum tensor in curved spacetimes:
- .
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