Foundations of Physics

, Volume 16, Issue 3, pp 267–293 | Cite as

Bianchi identities and the automatic conservation of energy-momentum and angular momentum in general-relativistic field theories

  • Friedrich W. Hehl
  • J. Dermott McCrea
Part II. Invited Papers Dedicated To John Archibald Wheeler


Automatic conservation of energy-momentum and angular momentum is guaranteed in a gravitational theory if, via the field equations, the conservation laws for the material currents are reduced to the contracted Bianchi identities. We first execute an irreducible decomposition of the Bianchi identities in a Riemann-Cartan space-time. Then, starting from a Riemannian space-time with or without torsion, we determine those gravitational theories which have automatic conservation: general relativity and the Einstein-Cartan-Sciama-Kibble theory, both with cosmological constant, and the nonviable pseudoscalar model. The Poincaré gauge theory of gravity, like gauge theories of internal groups, has no automatic conservation in the sense defined above. This does not lead to any difficulties in principle. Analogies to 3-dimensional continuum mechanics are stressed throughout the article.


Field Theory General Relativity Angular Momentum Gauge Theory Field Equation 
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Copyright information

© Plenum Publishing Corporation 1986

Authors and Affiliations

  • Friedrich W. Hehl
    • 1
    • 2
  • J. Dermott McCrea
    • 1
  1. 1.Department of Mathematical PhysicsUniversity CollegeDublin 4Ireland
  2. 2.Dublin Institute for Advanced StudiesDublin 4Ireland

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