So the curvature tensor has 20 independent elements whilst a solution of Einstein’s field equations determines the 10 independent elements of the Ricci tensor (a contraction of the 4 index curvature tensor first&last indices). This means that given a solution of the field equations the full curvature tensor is not uniquely deternined (pairs of Rijkl independent elements can be related to single or combinations of Rjk elements), does this mean anything physically?
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