No Arabic abstract
In the present paper, we consider a model of non-minimal modified Yang-Mills theory in the Friedmann-Robertson-Walker cosmology, in which the Yang-Mills field couples to the scalar curvature through a function of its first invariant. We show that cosmic acceleration can be realized due to non-minimal gravitational coupling of the modified Yang-Mills theory. Besides general study, we consider in detail the case of power-law coupling function. We derive the basic equations for the cosmic scale factor in our model, and provide several examples of their solutions.
We study a deSitter/Anti-deSitter/Poincare Yang-Mills theory of gravity in d-space-time dimensions in an attempt to retain the best features of both general relativity and Yang-Mills theory: quadratic curvature, dimensionless coupling and background independence. We derive the equations of motion for Lie algebra valued scalars and show that in the geometric optics limit they traverse geodesics with respect to the Lorentzian geometry determined by the frame fields. Mixing between components appears to next to leading order in the WKB approximation. We then restrict to two space-time dimensions for simplicity, in which case the theory reduces to the well known Katanaev-Volovich model. We complete the Hamiltonian analysis of the vacuum theory and use it to prove a generalized Birkhoff theorem. There are two classes of solutions: with torsion and without torsion. The former are parametrized by two constants of motion, have event horizons for certain ranges of the parameters and a curvature singularity. The latter yield a unique solution, up to diffeomorphisms, that describes a space constant curvature .
A modified version of the Ozer and Taha nonsingular cosmological model is presented on the assumption that the universes radius is complex if it is regarded as empty, but it contains matter when the radius is real. It also predicts the values: Omega_M =rho_M /rho_C approx 4/3, Omega_V = rho_V /rho_C approx 2/3, and Omega_ = rho_ /rho_C << 1 in the present nonrelativistic era, where rho_M = matter density, rho_V = vacuum density, rho_= negative energy density and rho_{C} = critical density.
Regular monopole and dyon solutions to the SU(2) Einstein Yang-Mills equations in asymptotically anti-de Sitter space are discussed. A class of monopole solutions are shown to be stable against spherically symmetric linear perturbations.
We discuss the relation between spacetime diffeomorphisms and gauge transformations in theories of the Yang-Mills type coupled with Einsteins General Relativity. We show that local symmetries of the Hamiltonian and Lagrangian formalisms of these generally covariant gauge systems are equivalent when gauge transformations are required to induce transformations which are projectable under the Legendre map. Although pure Yang-Mills gauge transformations are projectable by themselves, diffeomorphisms are not. Instead the projectable symmetry group arises from infinitesimal diffeomorphism-inducing transformations which must depend on the lapse function and shift vector of the spacetime metric plus associated gauge transformations. Our results are generalizations of earlier results by ourselves and by Salisbury and Sundermeyer.
In Einstein-Maxwell theory black holes are uniquely determined by their mass, their charge and their angular momentum. This is no longer true in Einstein-Yang-Mills theory. We discuss sequences of neutral and charged SU(N) Einstein-Yang-Mills black holes, which are static spherically symmetric and asymptotically flat, and which carry Yang-Mills hair. Furthermore, in Einstein-Maxwell theory static black holes are spherically symmetric. We demonstrate that, in contrast, SU(2) Einstein-Yang-Mills theory possesses a sequence of black holes, which are static and only axially symmetric.