Covariant Differential Identities and Conservation Laws in Metric-Torsion Theories of Gravitation. II. Manifestly Generally Covariant Theories

摘要

The present paper continues the work of the authors [arXiv:1306.6887[gr-qc]]. Here, we study generally covariant metric-torsion theories of gravitypresented more concretely, setting that their Lagrangians are \emph{manifestly}generally covariant scalars. It is assumed that Lagrangians depend on metrictensor, curvature tensor, torsion tensor and its first and second covariantderivatives, besides, on an arbitrary set of other tensor (matter) fields andtheir first and second covariant derivatives. Thus, both the standard minimalcoupling with the Riemann-Cartan geometry and non-minimal coupling with thecurvature and torsion tensors are considered. The studies and results are as follow. (a) A physical interpretation of theNoether and Klein identities is examined. It was found that they are the basisfor constructing equations of balance of energy-momentum tensors of varioustypes (canonical, metrical and Belinfante symmetrized). The equations ofbalance are presented. (b) Using the generalized equations of balance, new(generalized) manifestly generally covariant expressions for canonicalenergy-momentum and spin tensors of the matter fields are constructed. In thecases, when the matter Lagrangian contains both the higher derivatives andnon-minimal coupling with curvature and torsion, such generalizations arenon-trivial. (c) The Belinfante procedure is generalized for an arbitraryRiemann-Cartan space. (d) A more convenient in applications generalizedexpression for the canonical superpotential is obtained. (e) A total system ofequations for the gravitational fields and matter sources are presented in theform more naturally generalizing the Einstein-Cartan equations with matter.This result, being a one of more important results itself, is to be also abasis for constructing physically sensible conservation laws and theirapplications.