Summary
The weak-field approximation of the general relativity, which is made to fulfil all tests of post-Newtonian gravity, leads to a locally de Sitter invariant Yang-Mills theory of gravity in Minkowski space. As far as the approximations are concerned, the principle of general covariance is equivalent to the principle of local gauge symmetry. Einstein’s theory of general relativity appears to be a classical and zero-spin-density manifestation of this Yang-Mills theory.
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References
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Wang, M.J., Hsu, J.P. A Yang-Mills theory of gravity implied by general relativity. Nuov Cim A 107, 1229–1236 (1994). https://doi.org/10.1007/BF02775763
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DOI: https://doi.org/10.1007/BF02775763