2011/01/28 by L. V. Verozub, Leonid V. Verozub, Verozub, Leonid V.
Medicine · Physics and Astronomy · #Biofield Effects and Biophysics #Cosmology and Gravitation Theories #Cosmology and Nongalactic Astrophysics (astro-ph.CO) #FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc) #Relativity and Gravitational Theory #astro-ph.CO #gr-qc
paper · pdf · doi:10.48550/arxiv.1101.5536
7 pages, An error fixed in Section 3
openalex publication_date 2011/01/28 · arxiv created 2011/07/22 · arxiv updated 2011/07/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.