Cosmological Einstein-Yang-Mills equations

We use a systematic construction method for invariant connections on homogeneous spaces to find the Einstein-SU(n)-Yang-Mills equations for Friedmann-Robertson-Walker and locally rotationally symmetric homogeneous cosmologies. These connections depend on the choice of a homomorphism from the isotropy group into the gauge group. We consider here the cases of the gauge group SU(n) and SO(n) where these homomorphisms correspond to unitary or orthogonal representations of the isotropy group. For some of the simpler cases the full system of the evolution equations are derived, for others we only determine the number of dynamical variables that remain after some mild fixing of the gauge.Comment: 28 pages, uses amsmath,amsthm,amssymb,epsfig,verbatim, minor correction

Topological Black Holes of (n+1)-dimensional Einstein-Yang-Mills Gravity

We present the topological solutions of Einstein gravity in the presence of a non-Abelian Yang-Mills field. In ($n+1$) dimensions, we consider the $So(n(n-1)/2-1,1)$ semisimple group as the Yang-Mills gauge group, and introduce the black hole solutions with hyperbolic horizon. We argue that the 4-dimensional solution is exactly the same as the 4-dimensional solution of Einstein-Maxwell gravity, while the higher-dimensional solutions are new. We investigate the properties of the higher-dimensional solutions and find that these solutions in 5 dimensions have the same properties as the topological 5-dimensional solution of Einstein-Maxwell (EM) theory although the metric function in 5 dimensions is different. But in 6 and higher dimensions, the topological solutions of EYM and EM gravities with non-negative mass have different properties. First, the singularity of EYM solution does not present a naked singularity and is spacelike, while the singularity of topological Reissner-Nordstrom solution is timelike. Second, there are no extreme 6 or higher-dimensional black holes in EYM gravity with non-negative mass, while these kinds of solutions exist in EM gravity. Furthermore, EYM theory has no static asymptotically de Sitter solution with non-negative mass, while EM gravity has.Comment: 14 pages, 2 figures, accepted by Mod. Phys. Lett.

Topological Black Holes of Einstein-Yang-Mills dilaton Gravity

We present the topological solutions of Einstein-dilaton gravity in the presence of a non-Abelian Yang-Mills field. In 4 dimensions, we consider the $So(3)$ and $So(2,1)$ semisimple group as the Yang-Mills gauge group, and introduce the black hole solutions with spherical and hyperbolic horizons, respectively. The solution in the absence of dilaton potential is asymptotically flat and exists only with spherical horizon. Contrary to the non-extreme Reissner-Nordstrom black hole, which has two horizons with a timelike and avoidable singularity, here the solution may present a black hole with a null and unavoidable singularity with only one horizon. In the presence of dilaton potential, the asymptotic behavior of the solutions is neither flat nor anti-de Sitter. These solutions contain a null and avoidable singularity, and may present a black hole with two horizons, an extreme black hole or a naked singularity. We also calculate the mass of the solutions through the use of a modified version of Brown and York formalism, and consider the first law of thermodynamics.Comment: 13 pages, 3 figure

Leibnizian, Galilean and Newtonian structures of spacetime

The following three geometrical structures on a manifold are studied in detail: (1) Leibnizian: a non-vanishing 1-form $\Omega$ plus a Riemannian metric \h on its annhilator vector bundle. In particular, the possible dimensions of the automorphism group of a Leibnizian G-structure are characterized. (2) Galilean: Leibnizian structure endowed with an affine connection $\nabla$ (gauge field) which parallelizes $\Omega$ and \h. Fixed any vector field of observers Z ($\Omega (Z) = 1$), an explicit Koszul--type formula which reconstruct bijectively all the possible $\nabla$'s from the gravitational ${\cal G} = \nabla_Z Z$ and vorticity $\omega = rot Z/2$ fields (plus eventually the torsion) is provided. (3) Newtonian: Galilean structure with \h flat and a field of observers Z which is inertial (its flow preserves the Leibnizian structure and $\omega = 0$). Classical concepts in Newtonian theory are revisited and discussed.Comment: Minor errata corrected, to appear in J. Math. Phys.; 22 pages including a table, Late

Characterizing asymptotically anti-de Sitter black holes with abundant stable gauge field hair

In the light of the "no-hair" conjecture, we revisit stable black holes in su(N) Einstein-Yang-Mills theory with a negative cosmological constant. These black holes are endowed with copious amounts of gauge field hair, and we address the question of whether these black holes can be uniquely characterized by their mass and a set of global non-Abelian charges defined far from the black hole. For the su(3) case, we present numerical evidence that stable black hole configurations are fixed by their mass and two non-Abelian charges. For general N, we argue that the mass and N-1 non-Abelian charges are sufficient to characterize large stable black holes, in keeping with the spirit of the "no-hair" conjecture, at least in the limit of very large magnitude cosmological constant and for a subspace containing stable black holes (and possibly some unstable ones as well).Comment: 33 pages, 13 figures, minor change

Slowly Rotating Non-Abelian Black Holes

It is shown that the well-known non-Abelian static SU(2) black hole solutions have rotating generalizations, provided that the hypothesis of linearization stability is accepted. Surprisingly, this rotating branch has an asymptotically Abelian gauge field with an electric charge that cannot vanish, although the non-rotating limit is uncharged. We argue that this may be related to our second finding, namely that there are no globally regular slowly rotating excitations of the particle-like Bartnik-McKinnon solutions.Comment: 8 pages, LaTe

On the existence of dyons and dyonic black holes in Einstein-Yang-Mills theory

We study dyonic soliton and black hole solutions of the ${\mathfrak {su}}(2)$ Einstein-Yang-Mills equations in asymptotically anti-de Sitter space. We prove the existence of non-trivial dyonic soliton and black hole solutions in a neighbourhood of the trivial solution. For these solutions the magnetic gauge field function has no zeros and we conjecture that at least some of these non-trivial solutions will be stable. The global existence proof uses local existence results and a non-linear perturbation argument based on the (Banach space) implicit function theorem.Comment: 23 pages, 2 figures. Minor revisions; references adde