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