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The Einstein has following definition (in my course):

G_{με}= R_{με}- 1/2Rg_{με}.

But why don't we just:

g^{με}G_{με}= g^{με}R_{με}- 1/2Rg^{με}g_{με}.

<=>

G = R- 1/2 . R . 4 = R- 2R = -R? Is this wrong or.?

Also, what is the meaning of the ricci scalair and tensor?

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# Definition of the Einstein Tensor

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