Mathematics
Scientific paper
Oct 1977
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1977phrvd..16.2395n&link_type=abstract
Physical Review D - Particles and Fields, 3rd Series, vol. 16, Oct. 15, 1977, p. 2395-2401.
Mathematics
11
Einstein Equations, Gravitation Theory, Kinematics, Spin Dynamics, Astronomical Models, Gravitational Fields, Space-Time Functions, Transformations (Mathematics)
Scientific paper
It is proven that for any choice of minimally coupled source-field Lagrangian for the Einstein-Cartan-Sciama-Kibble theory of gravity, there exists a related minimally coupled source-field Lagrangian for the Einstein theory which produces the same field equations for the metric and source field. By using a standard first-order form for source Lagrangians, the converse is also demonstrated. This establishes a one-to-one correspondence between source Lagrangians for the two theories which clearly reveals their similarities and differences. Because of this 'equivalence,' one can view either theory, in terms of the other, as minimal coupling for a related Minkowski source Lagrangian or as nonminimal coupling for the same Minkowski source Lagrangian. Consequently the two theories are, in this sense, indistinguishable. Some other implications of this 'equivalence' are discussed.
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