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Einstein tensor : ウィキペディア英語版 | Einstein tensor
In differential geometry, the Einstein tensor (named after Albert Einstein; also known as the trace-reversed Ricci tensor) is used to express the curvature of a pseudo-Riemannian manifold. In general relativity, it occurs in the Einstein field equations for gravitation that describe spacetime curvature in a manner consistent with energy. == Definition == The Einstein tensor is a rank 2 tensor defined over pseudo-Riemannian manifolds. In index-free notation it is defined as :: where is the Ricci tensor, is the metric tensor and is the scalar curvature. In component form, the previous equation reads as :: The Einstein tensor is symmetric :: and, like the stress–energy tensor, divergenceless ::
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