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Main Question or Discussion Point
Why is Einstein's law of gravitation for empty space sometimes identified as Ricci tensor=0 instead of Einstein tensor=0. The first condition implies the second one, but not the other way around.
Not true. In vacuum the Einstein equations areWhy is Einstein's law of gravitation for empty space sometimes identified as Ricci tensor=0 instead of Einstein tensor=0. The first condition implies the second one, but not the other way around.
yes thats your problem I think. Its only in 4+ dimensions that you can have curvature in free space.Perhaps the equivalence of the two conditions is always true in 4-d space but not 2-d space..