Physics
Scientific paper
Nov 1981
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1981gregr..13.1037h&link_type=abstract
General Relativity and Gravitation, Volume 13, Issue 11, pp.1037-1056
Physics
73
Scientific paper
We continue our investigation of a variational principle for general relativity in which the metric tensor and the (asymmetric) linear connection are varied independently. As in Part I, the matter Lagrangian is minimally coupled to the connection and the gravitational Lagrangian is taken to be the curvature scalar, but we now relax the Riemannian constraint as far as possible—that is, as far as the projective invariance of the assumed gravitational Lagrangian will allow. The outcome of this procedure is a gravitational theory formulated in a volume-preserving space-time (i.e., with torsion and tracefree nonmetricity). The vanishing of the trace of the nonmetricity is due to the remaining vector constraint. We also discuss the physical significance of the relaxation of the Riemannian constraint, the possible relaxation of the vector constraint, the notion of the hypermomentum current, and its possible relation to elementary particle physics.
Hehl Friedrich W.
Lord Eric A.
Smalley Larry L.
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