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Einstein TensorIn differential geometry, the Einstein tensor is a 2-tensor defined over Riemannian manifolds and which is defined in index-free notation as, where is the Ricci tensor, is the metric tensor and is the Ricci scalar (or scalar curvature). In components, the above equation reads - ,
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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