Gauge theory of gravitation
Yang has laid the foundations for a ''gauge'' type theory of gravitation, reintroducing the Lagrangian previously considered by Weyl and Stephenson. In this paper, I develop the full theory using a variational principle on this Lagrangian with sources. Analysis of the full set of Euler-Lagrange equations shows that Einstein spaces satisfying R/sub mu//sub kappa/ = ..omega..g/sub mu//sub kappa/, with arbitrary cosmological constant ..omega.., are the only Riemannian vacuum solutions. This rules out the nonphysical, static, spherically symmetric solutions of Pavelle and Thompson; they only considered a subset of the Euler-Lagrange system of equations. The additional equations become important when sources to the gravitational field are considered. The full set of equations with sources have the following properties: The stress-energy tensor must be traceless. Other than a small exceptional class, all matter solutions must be non-Riemannian. The stress-energy tensor is not conserved if torsion is kept. The only Robertson-Walker cosmological solution which is Riemannian is static; all other homogeneous, isotropic cosmologies are non-Riemannian. The equations do not reduce to Poisson's equation for weak, static gravitational fields, thus violating the Newtonian limit. I finish by commenting on the ''conceptually superior ... integral formalism'' proposed by Yang and used as a foundation for his gauge-type gravitational theory. (AIP)
- Research Organization:
- McDonnell Center for the Space Sciences and Department of Physics, Washington University, St. Louis, Missouri 63130
- OSTI ID:
- 7355906
- Journal Information:
- Phys. Rev., D; (United States), Journal Name: Phys. Rev., D; (United States) Vol. 14:2; ISSN PRVDA
- Country of Publication:
- United States
- Language:
- English
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GAUGE INVARIANCE
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INVARIANCE PRINCIPLES
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LAGRANGIAN FUNCTION
MATHEMATICAL SPACE
PARTICLE PROPERTIES
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TENSORS
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