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It is shown that any theory of gravitation, based on the hypothesis of thegeodesic motion of test particles must be invariant under geodesic (projecive)mappings of the used space-time. The reason is that due to invariance of theequations of geodesic lines under a continuous group of transformations of thecoefficients of affine connection, there is a wide class of transformations ofthe geometrical objects of Riemannian space-time which leaves invariant theequations of motion of test particles. The FRW metric in cosmology and theSchwarzschild metric are a good example to make sure that the standardspace-time metrics does not determine the gravitational field unequivocally.

What is the meaning of non-uniqueness of FRW and Schwarzschild metrics?