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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 \mathbf is a rank 2 tensor defined over pseudo-Riemannian manifolds. In index-free notation it is defined as
::\mathbf=\mathbf-\frac\mathbfR,
where \mathbf is the Ricci tensor, \mathbf is the metric tensor and R is the scalar curvature. In component form, the previous equation reads as
::G_ = R_ - g_R .
The Einstein tensor is symmetric
::G_ = G_
and, like the stress–energy tensor, divergenceless
::\nabla_\mu G^ = 0\,.

抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)
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