Gauge theory of gravitation

Yang has laid the foundations for a "guage" 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 $R_{\mu \kappa }=\omega g_{\mu \kappa }$ 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.