A detailed study of the geometries that emerge by a gravitating generalized Yang monopole in even dimensions is carried out. In particular, those which present black hole and cosmological horizons. This two-horizon system is thermally unstable. The process of thermalization will drive both horizons to coalesce. This limit is what is profusely studied in this paper. It is shown that eventhough coordinate distance shrinks to zero, physical distance does not. So, there is some remaining space which geometry has been computed and identified as a generalized Nariai solution. The thermal properties of this new spacetime are then calculated. Topics, as the elliptical relation between radii of spheres in the geometry or a discussion about whether a mass-type term should be present in the line element or not, are also included.
We show that gravity cures the infra-red divergence of the Yang monopole when a proper definition of conserved quantities in curved backgrounds is used, i.e. the gravitating Yang monopole in cosmological Einstein theory has a finite mass in generic even dimensions (including time). In addition, we find exact Yang-monopole type solutions in the cosmological Einstein-Gauss-Bonnet-Yang-Mills theory and briefly discuss their properties.
We construct static axially symmetric solutions of SU(2) Einstein-Yang-Mills-Higgs theory in the topologically trivial sector, representing gravitating monopole--antimonopole pairs, linked to the Bartnik-McKinnon solutions.
In this paper we consider the presence of the Wu-Yang magnetic monopole in the global monopole spacetime and their influence on the vacuum polarization effects around these two monopoles placed together. According to Wu-Yang [Nucl. Phys. {\bf B107}, 365 (1976)] the solution of the Klein-Gordon equation in such an external field will not be an ordinary function but, instead, {\it section}. Because of the peculiar radial symmetry of the global monopole spacetime, it is possible to cover its space section by two overlapping regions, needed to define the singularity free vector potential, and to s…
A continuum of new monopole and dyon solutions in the Einstein-Yang-Mills theory in asymptotically anti-de Sitter space are found. They are regular everywhere and specified with their mass, and non-Abelian electric and magnetic charges. A class of monopole solutions which have no node in non-Abelian magnetic fields are shown to be stable against spherically symmetric linear perturbations.
In the pure Einstein-Yang-Mills theory in four dimensions there exist monopole and dyon solutions. The spectrum of the solutions is discrete in asymptotically flat or de Sitter space, whereas it is continuous in asymptotically anti-de Sitter space. The solutions are regular everywhere and specified with their mass, and non-Abelian electric and magnetic charges. In asymptotically anti-de Sitter space a class of monopole solutions have no node in non-Abelian magnetic fields, and are stable against spherically symmetric perturbations.
New static regular axially symmetric solutions of SU(2) Yang-Mills-Higgs theory are constructed. They are asymptotically flat and represent gravitating monopole-monopole pairs. The solutions form two branches linked to the second Bartnik-McKinnon solution on upper mass branch and to the unstable monopole-monopole configuration in flat space on the lower branch, respectively.
A continuum of monopole, dyon and black hole solutions exist in the Einstein-Yang-Mills theory in asymptotically anti-de Sitter space. Their structure is studied in detail. The solutions are classified by non-Abelian electric and magnetic charges and the ADM mass. The stability of the solutions which have no node in non-Abelian magnetic fields is established. There exist critical spacetime solutions which terminate at a finite radius, and have universal behavior. The moduli space of the solutions exhibits a fractal structure as the cosmological constant approaches zero.
We present two generic classes of supersymmetric solutions of N=2, d=4 supergravity coupled to non-Abelian vector supermultiplets with a gauge group that includes an SU(2) factor. The first class consists of embeddings of the 't Hooft-Polyakov monopole and in the examples considered it has a fully regular, asymptotically flat space-time metric without event horizons. The other class of solutions consists of regular non-Abelian extreme black holes. There is a covariant attractor at the horizon of these non-Abelian black holes.
Scaling behavior in the moduli space of monopole and dyon solutions in the Einstein-Yang-Mills theory in the asymptotically anti-de Sitter space is derived. The mass of monopoles and dyons scales with respect to their magnetic and electric charges, independent of the values of the cosmological constant and gauge coupling constant. The stable monopole and dyon solutions are approximated by solutions in the fixed anti-de Sitter spacetime. Unstable solutions can be viewed as the Bartnik-McKinnon solutions dressed with monopole and dyon solutions in the fixed anti-de Sitter space.
We discuss a non-minimal Einstein-Yang-Mills-Higgs model with uniaxial anisotropy in the group space associated with the Higgs field. We apply this theory to the problem of propagation of color and color-acoustic waves in the gravitational background related to the non-minimal regular Wu-Yang monopole.
We study spherically and axially symmetric monopoles of the SU(2) Einstein-Yang-Mills-Higgs-dilaton (EYMHD) system with a new coupling between the dilaton field and the covariant derivative of the Higgs field. This coupling arises in the study of (4+1)-dimensional vortices in the Einstein-Yang-Mills (EYM) system.
Schrödinger oscillators in a deformed point-like global monopole spacetime and a Wu-Yang magnetic monopole: position-dependent mass correspondence and isospectrality
Bertotti-Robinson spacetimes are topologically $AdS_2 \times S^2$ and described by a conformally flat metric. Together with the Coulomb electric potential, they provide a class of static, geodetically complete Einstein-Maxwell solutions. We show here that the Bertotti-Robinson metric together with Wu-Yang magnetic pole potentials give a class of static solutions of a system of non-minimally coupled Einstein-Yang-Mills equations that may be relevant for investigating vacuum polarization effects in a first order perturbative approach to quantum fields.
In this series of three papers, we generalize the derivation of dual photons and monopoles by Polyakov, and Banks, Myerson and Kogut, to obtain approximative models of SU(2) lattice gauge theory. Our approach is based on stationary phase approximations. In this second article, we start from the spin foam representation of 3-dimensional SU(2) lattice gauge theory. By extending an earlier work of Diakonov and Petrov, we approximate the expectation value of a Wilson loop by a path integral over a dual gluon field and monopole-like degrees of freedom. The action contains the tree-level Coulomb int…
We discuss new exact spherically symmetric static solutions to non-minimally extended Einstein-Yang-Mills equations. The obtained solution to the Yang-Mills subsystem is interpreted as a non-minimal Wu-Yang monopole solution. We focus on the analysis of two classes of the exact solutions to the gravitational field equations. Solutions of the first class belong to the Reissner-Nordstr{ö}m type, i.e., they are characterized by horizons and by the singularity at the point of origin. The solutions of the second class are regular ones. The horizons and singularities of a new type, the non-minimal o…
Preliminary results concerning the time evolution of strongly exited SU(2) Bogomolny-Prasad-Sommerfield (BPS) magnetic monopoles have been published in Phys. Rev. Lett. 92, 151801 (2004). The behavior of these dynamical magnetic monopoles was investigated by means of numerical simulations in the four dimensional Minkowski spacetime. The developed code incorporates both the techniques of conformal compactification and that of the hyperboloidal initial value problem. Our primary aim here is to provide a detailed account on the methods and results of the investigations reported in Phys. Rev. Lett…
We construct monopole-antimonopole chain and vortex solutions in Yang-Mills-Higgs theory coupled to Einstein gravity. The solutions are static, axially symmetric and asymptotically flat. They are characterized by two integers (m,n) where m is related to the polar angle and n to the azimuthal angle. Solutions with n=1 and n=2 correspond to chains of m monopoles and antimonopoles. Here the Higgs field vanishes at m isolated points along the symmetry axis. Larger values of n give rise to vortex solutions, where the Higgs field vanishes on one or more rings, centered around the symmetry axis. When…
Alternative theories of gravity and their solutions are of considerable importance since at some fundamental level the world can reveal new features. Indeed, it is suspected that the gravitational field might be nonminimally coupled to the other fields at scales not yet probed, bringing into the forefront nonminimally coupled theories. In this mode, we consider a nonminimal Einstein-Yang-Mills theory with a cosmological constant. Imposing spherical symmetry and staticity for the spacetime and a magnetic Wu-Yang ansatz for the Yang-Mills field, we find expressions for the solutions of the theor…
We show that the closed-form monotone solution linking two different vacuum states, for the exterior Yang--Mills wave equation over the extremal Reissner--Nordström spacetime found in a recent work of Bizoń and Kahl, is the unique solution to an associated domain-wall type energy minimization problem. We also derive the accompanying interior Yang--Mills wave equation within the same formalism. We obtain a few more closed-form solutions, regular and singular, among other solutions of oscillatory behavior, and discuss several interesting features of the solutions based on some energy considerati…
We prove the existence of the gravitating BPS monopole in Einstein-Yang-Mills-Higgs (EYMH) theory. Existence is established using a Newtonian perturbation argument which shows that a Yang-Mills-Higgs BPS monopole solution can be be continued analytically in powers of $1/c^{2}$ to an EYMH solution.
We construct monopole solutions in SU(2) Einstein-Yang-Mills-Higgs theory, carrying magnetic charge n. For vanishing and small Higgs selfcoupling, these multimonopole solutions are gravitationally bound. Their mass per unit charge is lower than the mass of the n=1 monopole. For large Higgs selfcoupling only a repulsive phase exists.
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 show that in an asymptotically flat space where an S-Matrix can be defined, dual supertranslations leave all its matrix elements invariant and the Hilbert space of asymptotic states factorizes into distinct super-selection sectors, labeled by their dual supertranslation charges. These results suggest that dual supertranslation may be interpreted as a redundant gauge symmetry of asymptotically flat spacetimes. This would allow to recast general relativity as a theory of diffeomorphisms possessing an additional asymptotic gauge symmetry. We then use the conjectured dual supertranslation gauge…
The behaviour of magnetic monopole solutions of the Einstein-Yang-Mills-Higgs equations subject to linear spherically symmetric perturbations is studied. Using Jacobi's criterion some of the monopoles are shown to be unstable. Furthermore the numerical results and analytical considerations indicate the existence of a set of stable solutions.
