Astronomy and Astrophysics – Astrophysics – General Relativity and Quantum Cosmology
Scientific paper
2011-01-28
Astronomy and Astrophysics
Astrophysics
General Relativity and Quantum Cosmology
7 pages, An error fixed in Section 3
Scientific paper
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.
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