Einstein Yang Mills Research Articles

Colored black holes and Kac-Moody algebra

We demonstrate that the near horizon symmetries of black holes in Einstein-Yang-Mills (EYM) theory are generated by an infinite-dimensional algebra that contains, in addition to supertranslations and superrotations, a non-Abelian loop algebra. This means that the Virasoro-Kac-Moody structure of EYM in asymptotically flat spacetimes has an exact analog in the near horizon region.

Off-shell extended graphic rule and the expansion of Berends-Giele currents in Yang-Mills theory

Tree-level color-ordered Yang-Mills (YM) amplitudes can be decomposed in terms of (n − 2)! bi-scalar (BS) amplitudes, whose expansion coefficients form a basis of Bern-Carrasco-Johansson (BCJ) numerators. By the help of the recursive expansion of Einstein-Yang-Mills (EYM) amplitudes, the BCJ numerators are given by polynomial functions of Lorentz contractions which are conveniently described by graphic rule. In this work, we extend the expansion of YM amplitudes to off-shell level. We define different types of off-shell extended numerators that can be generated by graphs. By the use of these extended numerators, we propose a general decomposition formula of off-shell Berends-Giele currents in YM. This formula consists of three terms: (i). an effective current which is expanded as a combination of the Berends-Giele currents in BS theory (The expansion coefficients are one type of off-shell extended numerators) (ii). a term proportional to the total momentum of on-shell lines and (iii). a term expressed by the sum of lower point Berends-Giele currents in which some polarizations and momenta are replaced by vectors proportional to off-shell momenta appropriately. In the on-shell limit, the last two terms vanish while the decomposition of effective current precisely reproduces the decomposition of on-shell YM amplitudes with the expected coefficients (BCJ numerators in DDM basis). We further symmetrize these coefficients such that the Lie symmetries are satisfied. These symmetric BCJ numerators simultaneously satisfy the relabeling property of external lines and the algebraic properties (antisymmetry and Jacobi identity).

A black hole solution of higher-dimensional Weyl–Yang–Kaluza–Klein theory

We consider the Weyl–Yang gauge theory of gravitation in a (4 + 3)-dimensional curved space-time within the scenario of the non-Abelian Kaluza–Klein theory for the source and torsion-free limits. The explicit forms of the field equations containing a new spin current term and the energy–momentum tensors in the usual four dimensions are obtained through the well-known dimensional reduction procedure. In this limit, these field equations admit (anti-)dyon and magnetic (anti-)monopole solutions as well as non-Einsteinian solutions in the presence of a generalized Wu–Yang ansatz and some specific warping functions when the extra dimensions associated with the round and squashed three-sphere S 3 are, respectively, included. The (anti-)dyonic solution has similar properties to those of the Reissner–Nordström–de Sitter black holes of the Einstein–Yang–Mills system. However, the cosmological constant naturally appears in this approach, and it associates with the constant warping function as well as the three-sphere radius. It is demonstrated that not only the squashing parameter ℓ behaves as the constant charge but also its sign can determine whether the solution is a dyon/monopole or an antidyon/antimonopole. It is also shown by using the power series method that the existence of nonconstant warping function is essential for finding new exact Schwarzschild-like solutions in the considered model.

Celestial operator products of gluons and gravitons

The operator product expansion (OPE) on the celestial sphere of conformal primary gluons and gravitons is studied. Asymptotic symmetries imply recursion relations between products of operators whose conformal weights differ by half-integers. It is shown, for tree-level Einstein–Yang–Mills theory, that these recursion relations are so constraining that they completely fix the leading celestial OPE coefficients in terms of the Euler beta function. The poles in the beta functions are associated with conformally soft currents.

Analytic non-Abelian gravitating solitons in the Einstein\u2013Yang\u2013Mills\u2013Higgs theory and transitions between them

Two analytic examples of globally regular non-Abelian gravitating solitons in the Einstein–Yang–Mills–Higgs theory in (3 + 1)-dimensions are presented. In both cases, the space-time geometries are of the Nariai type and the Yang–Mills field is completely regular and of meron type (namely, proportional to a pure gauge). However, while in the first family (type I) X_{0} = 1/2 (as in all the known examples of merons available so far) and the Higgs field is trivial, in the second family (type II) X_{0} = 1/2 is not 1/2 and the Higgs field is non-trivial. We compare the entropies of type I and type II families determining when type II solitons are favored over type I solitons: the VEV of the Higgs field plays a crucial role in determining the phases of the system. The Klein–Gordon equation for test scalar fields coupled to the non-Abelian fields of the gravitating solitons can be written as the sum of a two-dimensional D’Alembert operator plus a Hamiltonian which has been proposed in the literature to describe the four-dimensional Quantum Hall Effect (QHE): the difference between type I and type II solutions manifests itself in a difference between the degeneracies of the corresponding energy levels.

Evaluating EYM amplitudes in four dimensions by refined graphic expansion

The recursive expansion of tree level multitrace Einstein-Yang-Mills (EYM) amplitudes induces a refined graphic expansion, by which any tree-level EYM amplitude can be expressed as a summation over all possible refined graphs. Each graph contributes a unique coefficient as well as a proper combination of color-ordered Yang-Mills (YM) amplitudes. This expansion allows one to evaluate EYM amplitudes through YM amplitudes, the latter have much simpler structures in four dimensions than the former. In this paper, we classify the refined graphs for the expansion of EYM amplitudes into N k MHV sectors. Amplitudes in four dimensions, which involve k + 2 negative-helicity particles, at most get non-vanishing contribution from graphs in N k′ (k′ ≤ k) MHV sectors. By the help of this classification, we evaluate the non-vanishing amplitudes with two negative-helicity particles in four dimensions. We establish a correspondence between the refined graphs for single-trace amplitudes with left({g}_i^{-},{g}_j^{-}right) or left({h}_i^{-},{g}_j^{-}right) configuration and the spanning forests of the known Hodges determinant form. Inspired by this correspondence, we further propose a symmetric formula of double-trace amplitudes with left({g}_i^{-},{g}_j^{-}right) configuration. By analyzing the cancellation between refined graphs in four dimensions, we prove that any other tree amplitude with two negative-helicity particles has to vanish.

Quasinormal modes, quasiperiodic oscillations, and the shadow of rotating regular black holes in nonminimally coupled Einstein-Yang-Mills theory

In this paper we obtain an effective metric describing a regular and rotating magnetic black hole (BH) solution with a Yang-Mills electromagnetic source in Einstein-Yang-Mills (EYM) theory using the Newman--Janis algorithm via the non-complexification radial coordinate procedure. We then study the BH shadow and the quasinormal modes (QNMs) for massless scalar and electromagnetic fields and the quasiperiodic oscillations (QPOs). To this end, we also study the embedding diagram for the rotating EYM BH. The energy conditions, shadow curvature radius, topology and the dynamical evolution of scalar and electromagnetic perturbations using the time domain integration method are investigated. We show that the shadow radius decreases by increasing the magnetic charge, while the real part of QNMs of scalar and electromagnetic fields increases by increasing the magnetic charge. This result is consistent with the inverse relation between the shadow radius and the real part of QNMs. In addition, we have studied observational constraints on the EYM parameter $\lambda$ via frequency analysis of QPOs and the EHT data of shadow cast by the M87 central black hole. We also find that the decaying rate of the EYM BH is slower than that of the neutral and ends up with a tail. We argue that the rotating EYM black hole can be distinguished from the Kerr-Newman black hole with a magnetic charge based on the difference between the angular diameters of their shadows.

Two-uniqueness of rational ghost soliton solution and well-posedness of perturbed Einstein-Yang-Mills equations

<abstract><p>In this paper, we discuss the uniqueness and existence of local solutions for the perturbed static, spherically symmetric Einstein-Yang-Mills (EYM) equations with gauge group $ SU(2) $. Moreover, we show that the rational expression solutions to the equations only happened in traditional Schwarzschild solutions and Reissner-Nordstrom solutions. From these results, we can infer that there is no rational ghost soliton solution for the EYM equations.</p></abstract>

Anisotropic Einstein Yang-Mills Higgs dark energy

In the context of the dark energy scenario, the Einstein Yang-Mills Higgs model in the SO(3) representation was studied for the first time by M. Rinaldi (see [1]) in a homogeneous and isotropic spacetime. We revisit this model, finding in particular that the interaction between the Higgs field and the gauge fields generates contributions to the momentum density, anisotropic stress and pressures, thus making the model inconsistent with the assumed background. We instead consider a homogeneous but anisotropic Bianchi-I space-time background in this paper and analyze the corresponding dynamical behaviour of the system. We find that the only attractor point corresponds to an isotropic accelerated expansion dominated by the Higgs potential. However, the model predicts non-negligible anisotropic shear contributions nowadays, i.e. the current Universe can have hair although it will loose it in the future. We investigate the evolution of the equation of state for dark energy and highlight some possible consequences of its behaviour related to the process of large-scale structure formation. As a supplement, we propose the “Higgs triad” as a possibility to make the Einstein Yang-Mills Higgs model be consistent with a homogeneous and isotropic spacetime.

Lorentzian Symmetric Spaces Which are Einstein–Yang–Mills with Respect to Invariant Metric Connections

We classify four-dimensional connected simply-connected Lorentzian symmetric spaces M with connected nontrivial isotropy group furnishing solutions of the Einstein–Yang–Mills equations. Those solutions are built with respect to some invariant metric connection $$\Lambda $$ in the bundle of orthonormal frames of M and some diagonal metric on the holonomy algebra corresponding to $$\Lambda $$ .

A graphic approach to identities induced from multi-trace Einstein-Yang-Mills amplitudes

Symmetries of Einstein-Yang-Mills (EYM) amplitudes, together with the recursive expansions, induce nontrivial identities for pure Yang-Mills amplitudes. In the previous work [1], we have already proven that the identities induced from tree level single-trace EYM amplitudes can be precisely expanded in terms of BCJ relations. In this paper, we extend the discussions to those identities induced from all tree level multi-trace EYM amplitudes. Particularly, we establish a refined graphic rule for multi-trace EYM amplitudes and then show that the induced identities can be fully decomposed in terms of BCJ relations.

P-wave holographic superconductors with massive vector condensate in Born\u2013Infeld electrodynamics

In this paper, we have studied the effect of Born–Infeld electrodynamics in holographic p-wave superconductors with massive vector condensation. We have analysed this model in the probe limit using a variational method known as the Stürm–Liouville eigenvalue approach. For this p-wave holographic superconductor model, we have calculated the critical temperature T_{c} as well as the value of the condensation operator for two different choices of m^{2}. We have also pointed out the similarities and dissimilarities between this model for m^{2} = 0 and p-wave holographic superconductor model constructed out of Einstein–Yang–Mills theory. We have then computed the conductivity of these holographic superconductor models using a self-consistent approach and have shown that the DC conductivity diverges.

Stable thin-shells from 5-dimensional extremal Einstein–Yang–Mills fields

By employing exact Einstein–Yang–Mills (EYM) solution in [Formula: see text] dimensions we establish spherical thin-shells with mass and Yang–Mills charge. Remarkably these shells are stable against linear, radial perturbations with a barotropic fluid presented on the shell with a generic equation of state [Formula: see text] supporting the speed of sound [Formula: see text].

Dyonic black holes in anti-de Sitter Einstein–Yang–Mills theory, characterised by an infinite set of global charges

We here derive field equations for static, spherically symmetric, dyonic Einstein–Yang–Mills theory with a negative cosmological constant . We are able to find new non-trivial black hole solutions to this system in two regimes: where the gauge fields are small; and where . We also show that some may be uniquely characterised by a countably infinite set of asymptotically-defined charges. This may have implications for Bizon’s modified ‘No Hair’ conjecture.

What Are Observables in Hamiltonian Einstein\u2013Maxwell Theory?

Is change missing in Hamiltonian Einstein–Maxwell theory? Given the most common definition of observables (having weakly vanishing Poisson bracket with each first-class constraint), observables are constants of the motion and nonlocal. Unfortunately this definition also implies that the observables for massive electromagnetism with gauge freedom (‘Stueckelberg’) are inequivalent to those of massive electromagnetism without gauge freedom (‘Proca’). The alternative Pons–Salisbury–Sundermeyer definition of observables, aiming for Hamiltonian–Lagrangian equivalence, uses the gauge generator G, a tuned sum of first-class constraints, rather than each first-class constraint separately, and implies equivalent observables for equivalent massive electromagnetisms. For General Relativity, G generates 4-dimensional Lie derivatives for solutions. The Lie derivative compares different space-time points with the same coordinate value in different coordinate systems, like 1 a.m. summer time versus 1 a.m. standard time, so a vanishing Lie derivative implies constancy rather than covariance. Requiring equivalent observables for equivalent formulations of massive gravity confirms that G must generate the 4-dimensional Lie derivative (not 0) for observables. These separate results indicate that observables are invariant under internal gauge symmetries but covariant under external gauge symmetries, but can this bifurcated definition work for mixed theories such as Einstein–Maxwell theory? Pons, Salisbury and Shepley have studied G for Einstein–Yang–Mills. For Einstein–Maxwell, both F_{mu nu } and g_{mu nu } are invariant under electromagnetic gauge transformations and covariant (changing by a Lie derivative) under 4-dimensional coordinate transformations. Using the bifurcated definition, these quantities count as observables, as one would expect on non-Hamiltonian grounds.

Probing a regular non-minimal Einstein-Yang-Mills black hole with gravitational lensings

We investigate weak and strong deflection gravitational lensings of the regular black hole predicted by a non-minimal Einstein–Yang–Mills theory. We find that its weak deflection lensing is the same as a Reissner–Nordström black hole's. Observables in the strong deflection lensing, including the apparent radius of the photon sphere (shadow) as well as the angular separation, brightness difference and time delay between relativistic images, are obtained and analyzed for the supermassive black holes Sgr A* and M87* in the Galactic Center and at the center of M87. We find that only the apparent radii of the photon spheres are within the ability of current technology, whereas there is not enough resolution to distinguish the regular Einstein–Yang–Mills black hole from the Reissner–Nordström one. Meanwhile, caution needs to be paid when the diameter of M87*'s shadow measured by the Event Horizon Telescope is directly taken to constrain such a regular black hole.

A graphic approach to gauge invariance induced identity

All tree-level amplitudes in Einstein-Yang-Mills (EYM) theory and gravity (GR) can be expanded in terms of color ordered Yang-Mills (YM) ones whose coefficients are polynomial functions of Lorentz inner products and are constructed by a graphic rule. Once the gauge invariance condition of any graviton is imposed, the expansion of a tree level EYM or gravity amplitude induces a nontrivial identity between color ordered YM amplitudes. Being different from traditional Kleiss-Kuijf (KK) and Bern-Carrasco-Johansson (BCJ) relations, the gauge invariance induced identity involves polarizations in the coefficients. In this paper, we investigate the relationship between the gauge invariance induced identity and traditional BCJ relations. By proposing a refined graphic rule, we prove that all the gauge invariance induced identities for single trace tree-level EYM amplitudes can be precisely expanded in terms of traditional BCJ relations, without referring any property of polarizations. When further considering the transversality of polarizations and momentum conservation, we prove that the gauge invariance induced identity for tree-level GR (or pure YM) amplitudes can also be expanded in terms of traditional BCJ relations for YM (or bi-scalar) amplitudes. As a byproduct, a graph-based BCJ relation is proposed and proved.

Black holes in magnetic monopoles with a dark halo

We study a spontaneously broken Einstein–Yang–Mills–Higgs model coupled via a Higgs portal to an uncharged scalar [Formula: see text]. We present a phase diagram of self-gravitating solutions showing that depending on the choice of parameters of the [Formula: see text] scalar potential and the Higgs portal coupling constant [Formula: see text], one can identify different regions: If [Formula: see text] is sufficiently small, a [Formula: see text] halo is created around the monopole core which in turn surrounds a black hole. For larger values of [Formula: see text], no halo exists and the solution is just a black hole monopole one. When the horizon radius grows and becomes larger than the monopole radius, solely a black hole solution exists. Because of the presence of the [Formula: see text] scalar, a bound for the Higgs potential coupling constant exists and when it is not satisfied, the vacuum is unstable and no nontrivial solution exists. We briefly comment on possible connections of our results with those found in recent dark matter axion models.

Absorption Cross Section and Decay Rate of Dilatonic Black Strings

We studied in detail the propagation of a massive tachyonic scalar field in the background of a five-dimensional (5D) Einstein–Yang–Mills–Born–Infeld–dilaton black string: the massive Klein–Gordon equation was solved, exactly. Next we obtained complete analytical expressions for the greybody factor, absorption cross section, and decay rate for the tachyonic scalar field in the geometry under consideration. The behaviors of the obtained results are graphically represented for different values of the theory’s free parameters. We also discuss why tachyons should be used instead of ordinary particles for the analytical derivation of the greybody factor of the dilatonic 5D black string.

Regular solutions in f(T) -Yang-Mills theory

We consider extended covariant teleparallel $(f(T))$ gravity whose action is analytic in the torsion scalar and which is sourced by an $su(2)$ valued Yang-Mills field. Specifically, we search for regular solutions to the coupled $f(T)$ Yang-Mills system. For $f(T)=T$ we, not surprisingly, recover the Bartnik-McKinnon solitons of Einstein Yang-Mills theory. However, interesting effects are discovered with the addition of terms in the action which are nonlinear in the torsion scalar, which we specifically study up to cubic order. With the addition of the nonlinear terms the number of regular solutions becomes finite. As well, beyond critical values of the coupling constants we find that there exist \emph{no} regular solutions. These behaviors are asymmetric with respect to the sign of the nonlinear coupling constants and the elimination of regular solutions turns out to be extremely sensitive to the presence of the cubic coupling. It may be possible, therefore, that with sufficiently high powers of torsion in the action, there may be no regular Yang-Mills static solutions.