# After finding the Einstein Tensor

Before I begin, I stress that this is NOT a homework question but rather a self-study question.

In any case, I calculated the Einstein Tensor of a body with the metric diag[{2GM/r-1,0,0,0},{0,1+2GM/r,0,0},{0,0,1+2GM/r,0},{0,0,0,1+2GM/r}]. What does the Einstein Tensor represent? Does its determinant/trace/or matrix operations have any physical meaning?

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Basically, the Einstein tensor is a trace-reversed version of the Ricci tensor (a contraction of the Riemann curvature tensor). Its most salient feature is that it is conserved, in the following sense: $$G^{ab}_{;b} = 0$$. In other words, the "divergence" of the Einstein tensor vanishes.