Global charges of stationary non-Abelian black holes

We consider stationary axially symmetric black holes in SU(2) Einstein-Yang-Mills-dilaton theory. We present a mass formula for these stationary non-Abelian black holes, which also holds for Abelian black holes. The presence of the dilaton field allows for rotating black holes, which possess nontrivial electric and magnetic gauge fields, but do not carry a non-Abelian charge. We further present a new uniqueness conjecture.     

Domain with Noncompactified Extra Dimensions in the Multidimensional Universe with Compactified Extra Dimensions

It is argued that in our Universe with compactified extra dimensions (ED) also domains exist with noncompactified ED. The multidimensional gravity (MD) on the principal bundle with structural group SU(3) is considered and a spherically symmetric solution in this theory is obtained. This solution is a wormhole-like object located between two null surfaces ds² = 0 and can be considered as a domain with noncompactified ED which is sewn to a 4D spacetime with compactified ED. In some sense these solutions are dual to black holes: they represent static spherically symmetric solutions under null surfaces, whereas black holes are static spherically symmetric solutions outside the event horizon.     

耦合SU(5) EYMH系统的静态双荷黑洞

研究耦合ＳＵ（５）Ｅｉｎｓｔｅｉｎ－Ｙａｎｇ－Ｍｉｌｌｓ－Ｈｉｇｇｓ（ＥＹＭＨ）系统。得到了场方程的一类静态球对称Ｒｅｉｓｓｎｅｒ－Ｎｏｒｄｓｔｒｏｍ（Ｒ－Ｎ）型解，它代表具有ＳＵ（５）双荷子（磁荷为±3/(2e)）的静态黑洞。 关键词：     

Asymptotically de Sitter and anti-de Sitter black holes with confining electric potential

We study gravity interacting with a special kind of QCD-inspired nonlinear gauge field system which earlier was shown to yield confinement-type effective potential (the “Cornell potential”) between charged fermions (“quarks”) in flat space-time. We find new static spherically symmetric solutions generalizing the usual Reissner-Nordström-de Sitter and Reissner-Nordström-anti-de Sitter black holes with the following additional properties: (i) appearance of a constant radial electric field (in addition to the Coulomb one); (ii) novel mechanism of dynamical generation of cosmological constant through the non-Maxwell gauge field dynamics; (iii) appearance of confining-type effective potential in charged test particle dynamics in the above black hole backgrounds.     

“Charged” particle’s tunneling from rotating black holes

The behavior of a scalar field theory near the event horizon in a rotating black hole background can be effectively described by a two dimensional field theory in a gauge field background. Based on this fact, we proposal that the quantum tunneling from rotating black hole can be treated as “charged” particle’s tunneling process in its effectively two dimensional metric. Using this viewpoint and considering the corresponding “gauge charge” conservation, we calculate the non-thermal tunneling rate of Kerr black hole and Myers–Perry black hole, and results are consistent with Parikh–Wilczek’s original result for spherically symmetric black holes. Especially for Myers–Perry black hole which has multi-rotation parameters, our calculation fills in the gap existing in the literature applying Parikh–Wilczek’s tunneling method to various types black holes. Our derivation further illuminates the essential role of effective gauge symmetry in Hawking radiation from rotating black holes.     

Exact SU(n) instantons with cylindrical symmetry

We construct SO(3) symmetric, irreducible instantons in an SU(n) gauge theory. The solutions are symmetric with respect to J = ?ir × ? + T, where T spans the maximal SO(3) subalgebra of SU(n). Our ansatz as well as the resulting self dual equations are closely related to those for monopoles.     

Topology and lattice gauge fields

A general discussion of the topology of continuum gauge fields and the problems involved in defining and computing the topology of a lattice gauge field configuration is given. Two definitions of the topological charge for 4-dimensional SU(n) lattice gauge theory are presented. The first of these is geometrically the most straightforward, the second the most useful for efficient numerical calculations.     

Abundant stable gauge field hair for black holes in anti-de Sitter space

We present new hairy black hole solutions of SU(N) Einstein-Yang-Mills (EYM) theory in asymptotically anti-de Sitter (AdS) space. These black holes are described by N+1 independent parameters and have N-1 independent gauge field degrees of freedom. Solutions in which all gauge field functions have no zeros exist for all N, and for a sufficiently large (and negative) cosmological constant. At least some of these solutions are shown to be stable under classical, linear, spherically symmetric perturbations. Therefore there is no upper bound on the amount of stable gauge field hair with which a black hole in AdS can be endowed.     

Black holes in N=8 supergravity

Solutions of the bosonic field equations of the ungauged, N=8 supergravity which describe black holes with no scalar hairs are obtained. It is found that, in contrast to the Einstein-Maxwell theory where a uniqueness theorem exists, there are two distinct families of black holes in N=8 supergravity. There are also two distinct generalizations of Majumdar-Papapertrou solutions which describe the static equilibrium of many black holes.     

Multidimensional Gravity on the Principal Bundles

The multidimensional gravity on the total space of principal bundles is considered. In this theory the gauge fields arise as nondiagonal components of a multidimensional metric. The spherically symmetric and cosmological solutions for gravity on an SU(2) principal bundle are obtained. The static spherically symmetric solution is a wormhole-like solution located between two null surfaces, in contrast to 4D Einstein-Yang-Mills theory where the corresponding solution (black hole) is located outside of the event horizon. The cosmological solution has (at least locally) the bouncing-off effect for the spatial dimensions.     

SU(2) gauge symmetry and anomaly of the S = 12 antiferromagnetic Heisenberg model in 2 + 1 dimensions

On the basis of the local SU (2) symmetry of the Heisenberg model, we show that the model, in a continuum limit, reduces to a problem of massless fermions coupled to an SU(2) gauge field in three space-time dimensions. The effective gauge field action changes by ± π ⦶ n ⦶ under a large gauge transformation with winding number n. To restore the gauge invariance, a parity- nonconserving, topological term is needed in the effective action. The physical implications are conjectured.     

The Thermal Radiation from Static Spherically Symmetric Black Holes

By use of the radiant emittance near the event horizon of static spherically symmetric black hole, the radiation field around the black hole was studied and found the generalized Stefan Boltzmann coefficient σ of thermal radiation near the event horizon is much greater than the flat space-time blackbody radiation. For Schwarzschild black hole, σ will increased as the black hole mass increases. For Reissner-Nordström black hole, σ has some relation with the quality and the charges of the black hole. Thermal particle model was proposed creatively to study the radiation power and radiant energy flux of static spherically symmetric black hole, found when η take the inherent thickness, for all Schwarzschild black hole the radiation power are the same and the radiant energy flux is inversely proportional to the square of the distance from observer to the black hole, for Reissner-Nordström black hole the radiation power is associated with the quality and the charge of the black hole. When given the mass and charges of the black hole, the radiant energy flux is inversely proportional to the square of the distance from observer to the black hole.     

Stability of higher-dimensional Einstein-Yang-Mills theories on symmetric spaces

We study (4 + d)-dimensional Einstein-Yang-Mills theories with arbitrary gauge groups, G_YM. The theory is compactified on a d-dimensional symmetric coset space $\text{G}\text{H}$ with a symmetric, topologically non-trivial classical gauge field, embedded in an H-subgroup of the Yang-Mills group. These theories are known to be classically stabilized by gravity if G_YM = H, $\text{G}\text{H}$ is a sphere and d ≠ 3. We study classical instabilities caused by embedding H in a larger gauge group. The small fluctuation spectrum is completely calculable, and leads to a stability condition. For two-dimensional spheres this condition is precisely the Brandt-Neri stability condition for non-abelian monopole fields. For four-spheres we find stability for SU(2) instantons embedded in arbitrary gauge groups and we reproduce the fluctuation spectrum around instantons. For higher-dimensional spheres the stable solutions of this type are completely classified, and occur only for d = 5, 6, 8, 9, 10, 12 and 16. The results show a remarkable agreement with expected topological stability. We also give a few examples with other symmetric spaces, such as CP_n, where the stability criterion appears less restrictive.     

A no-hair theorem for spherically symmetric black holes in $$R^2$$ gravity

In a recent paper Cañate (Class Quantum Grav 35:025018, 2018) proved a no hair theorem to static and spherically symmetric or stationary axisymmetric black holes in general f(R) gravity. The theorem applies for isolated asymptotically flat or asymptotically de Sitter black holes and also in the case when vacuum is replaced by a minimally coupled source having a traceless energy momentum tensor. This theorem excludes the case of pure quadratic gravity, \(f(R) = R^2\). In this paper we use the scalar tensor representation of general f(R) theory to show that there are no hairy black hole in pure \(R^2\) gravity. The result is limited to spherically symmetric black holes but does not assume asymptotic flatness or de-Sitter asymptotics as in most of the no-hair theorems encountered in the literature. We include an example of a static and spherically symmetric black hole in \(R^2\) gravity with a conformally coupled scalar field having a Higgs-type quartic potential.     

Anomaly analysis of Hawking radiation from Kaluza–Klein black hole with squashed horizon

Considering gravitational and gauge anomalies at the horizon, a new method to derive Hawking radiation from black holes has been developed by Wilczek et al. In this paper, we apply this method to non-rotating and rotating Kaluza–Klein black holes with squashed horizon, respectively. For the rotating case, we found that, after dimensional reduction, an effective U(1) gauge field is generated by an angular isometry. The results show that the gauge current and energy-momentum tensor fluxes are exactly equivalent to Hawking radiation from the event horizon.     

Compactification of Einstein-Yang-Mills theories on CPn

We study compactification of Einstein-Yang-Mills theories in 2n + 4 dimensions on the manifold CP_n, with a classical gauge field that is equal to the spin connection. The complete boson fluctuation spectrum is calculated and no tachyons, ghosts or massless scalars are found for the minimal Yang-Mills group SU(n) × U(1). For larger groups, tachyons or massless scalars may appear.     

Supermembranes on black holes

We report a new family of supermembrane vacua possesing the Siegel symmetry. This family consists of bosonic solutions of supermembrane field equations and describes static, toroidal membranes in d=11 black hole spacetimes. The black holes we consider are obtained by embedding the d=4 Reissner-Nordström solutions into d=11, N=1 supergravity. We show that supermembranes pick, as their backgrounds, only the extreme Reissner-Nordström black holes and require the d=4 magnetic charge to be non-zero. Moreover, the membranes on dyonic holes can be interpreted, at the linearized level, as fluctuations of the membranes on magnetically charged holes. The quantisation around the toroidal membranes on the magnetically charged, extreme black holes therefore poses itself as an interesting problem.     

An operatorially solved model of massless two-dimensional quantum chromodynamics

An operator solution is constructed in (1,1) dimensions to the massless quantum chromodynamics of n fermion quarks and n² ? 1 vector boson gluons with local colour SU(n) symmetry. The interacting quark field is a confined SU(n) Thirring field with zero Abelian coupling. The colour gluons are dependent Lie fields obeying the gluon-free fermionic current identity. Explicit local infinitesimal operator colour transformations (with an arbitrary coordinate-independent Lorentz vector coefficient defining the gauge) are given and the requirement of proper colour covariance linked to the vanishing of the coloured quark source currents and hence to the absence of coloured quark-composite states. The status of Noether's theorem is also clarified.     

Cylindrically and spherically symmetric monopoles in SU(3) gauge theory

We apply to the Atiyah-Ward ansätze a systematic procedure locating symmetric monopoles in SU(3) gauge theory broken to U(1) × U(1). In particular we recover the known spherically symmetric monopole as a limit of a cylindrically symmetric separated two monopole solution in SU(3). We also discuss the spherically symmetric monopole in SU(n). This latter is the only instance where we have properly shown the smoothness of the Higgs and gauge fields.     

Multidimensional geometric models of electric and color charges with detachment of supplementary coordinates

A geometric model of electric charge is proposed. In this model there is a "naked" charge shunted by a "fuzz" of virtual necks. The "naked" charge is a 5-dimensional neck solution in Kaluza-Klein theory. Detachment of the supplementary coordinates occurs on the two spheres (null surfaces) bounding this neck which allows fastening two Reissner-Nordstrom black holes at both sides of it. The virtual necks entrap some of the field lines emerging from the "naked" charge. This effect can significantly reduce the apparent charge at infinity up to the real relation m² < e² for the electron. A similar construction is also presented for the color gauge SU(2) charge. Kirgiz State National University. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 2, pp. 7–11, February, 1998.