Thus another name for the Einstein tensor is the " trace-reversed Ricci tensor ".
2.
The left hand side, the Einstein tensor, can be thought of as a kind of average curvature.
3.
To get physical results, we can either turn to perturbation methods or linear approximations of the Einstein tensor.
4.
We have got about half the material we need to formulate the Einstein equations, namely, the Einstein tensor.
5.
Now that we have postulated the metric tensor, we have a lot of algebra to do in order to arrive at the Einstein tensor.
6.
Then, each set of tensor elements may be symbollically coded, until one finally has got symbollic expressions for all 4 x 4 = 16 components of the Einstein tensor.
7.
On the left-hand side is the Einstein tensor, a specific divergence-free combination of the Ricci tensor R _ { \ mu \ nu } and the metric.
8.
This implies that the curvature of space ( represented by the Einstein tensor ) is directly connected to the presence of matter and energy ( represented by the stress energy tensor ).
9.
In the special case of a locally inertial reference frame near a point, the first derivatives of the metric tensor vanish and the component form of the Einstein tensor is considerably simplified:
10.
The EFE describe how mass and energy ( as represented in the stress energy tensor ) are related to the curvature of space-time ( as represented in the Einstein tensor ).
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