Abstract
Einstein's equations are rewritten in terms of a certain torsionless linear connection Γα βμ which differs, in general, from the Levi-Civita metric connection γα βμ. The torsionless connection Γα βμ appears in a natural way as the canonical momentum of the gravitational field gμν . Einstein's equations have a simple interpretation in terms of the connection Γα βμ. The equivalence of the so-calledpurely metric, purely affine, andmetricaffine theories of gravitation is proved.
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This work has been written under the financial support of Gruppo Nazionale per la Fisica Matematica of the Italian National Research Council.
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Ferraris, M., Kijowski, J. On the equivalence of the relativistic theories of gravitation. Gen Relat Gravit 14, 165–180 (1982). https://doi.org/10.1007/BF00756921
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DOI: https://doi.org/10.1007/BF00756921