Generalized Einstein-Cartan field equations

Details Generalized Einstein-Cartan field equations Generalized Einstein-Cartan field equations

Dec 1976

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1976phrvd..14.3314s&link_type=abstract

Physical Review D (Particles and Fields), Volume 14, Issue 12, 15 December 1976, pp.3314-3321

Physics

11

Scientific paper

Field equations are studied for generalized Einstein-Cartan-Sciama-Kibble (EC) theories in which the connection is not necessarily compatible with the metric and the Lagrangian is not necessarily the curvature scalar. The condition that the Euler-Lagrange equations for a general Lagrangian density L(g, ∂g,∂∂g, Γ, ∂Γ) involve no third- or higher-order derivatives of the metric requires that the gravitational field equations be equivalent to those of general relativity with modified sources. The divergence of the symmetric "energymomentum" tensor δLmatterδg(ij) evaluated with δ(Γlmn-lmn)=0 for a generalized EC theory does not vanish in the presence of spin. The general form of the spin field equation linear in the defect λijk≡Γijk-ijk is derived.

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