Einstein–Yang–Mills–Higgs Research Articles

Asymptotic behaviour of the Einstein-Yang-Mills-Higgs system in a Bianchi type I model

We study the Einstein-Yang-Mills-Higgs (EYMH) system with a positive cosmological constant in the Bianchi type I space-time with locally rotational symmetry (LRS). In particular, we consider the nonlinear interaction of the Higgs field with the Yang-Mills field coupled to an unknown gravitational field. For the considered model, from certain additional conditions (the temporal gauge and some symmetries), we derive the conservation laws for the field equations and we then deduce the exact formulation of equations in the geometric framework. Furthermore, using an iterative approch and some mathematical analysis tools, we study the above system of equations. We then establish a global existence result for the homogeneous solution and we analyse its asymptotic behaviour.

Gravitating magnetic monopole via the spontaneous symmetry breaking of pure R2 gravity

The pure $R^2$ gravity is equivalent to Einstein gravity with cosmological constant and a massless scalar field and it further possesses the so-called restricted Weyl symmetry which is a symmetry larger than scale symmetry. To incorporate matter, we consider a restricted Weyl invariant action composed of pure $R^2$ gravity, SU(2) Yang-Mills fields and a non-minimally coupled massless Higgs field (a triplet of scalars). When the restricted Weyl symmetry is spontaneously broken, it is equivalent to an Einstein-Yang-Mills-Higgs (EYMH) action with a cosmological constant and a massive Higgs non-minimally coupled to gravity i.e. via a term $\tilde{\xi} R |\Phi|^2$. When the restricted Weyl symmetry is not spontaneously broken, linearization about Minkowski space-time does not yield gravitons in the original $R^2$ gravity and hence it does not gravitate. However, we show that in the broken gauge sector of our theory, where the Higgs field acquires a non-zero vacuum expectation value, Minkowski space-time is a viable gravitating background solution. We then obtain numerically gravitating magnetic monopole solutions for non-zero coupling constant $\tilde{\xi}=1/6$ in three different backgrounds: Minkowski, anti-de Sitter (AdS) and de Sitter (dS), all of which are realized in our restricted Weyl invariant theory.

Gravitating dyons in Vaidya geometry

Gravitating monopoles and dyons in Einstein–Yang–Mills (EYM) or Einstein–Yang–Mills–Higgs (EYMH) systems have been extensively studied for various curved space–times, including those of black holes. We construct dyonic solutions of the EYMH theory in Vaidya space–time using a set of generalized Julia–Zee ansatz for the fields. It is found that the dyonic charge is static in nature and it does not contribute to the energy of the null dust.

On the constraints problem for the Einstein–Yang–Mills–Higgs system

We provide proofs of some key propositions that were used in previous work by Dossa and Tadmon dealing with the characteristic initial value problem for the Einstein–Yang–Mills–Higgs (EYMH) system. The aforesaid proofs were missing, making the considered work difficult to understand. This work is presented with a view to have an almost self-contained paper. With this respect we completely recall the process of constructing initial data for the EYMH system on two intersecting smooth null hypersurfaces as done in the work of Dossa and Tadmon mentioned above. This is achieved by successfully adapting the hierarchical method set up by Rendall to solve the same problem for the Einstein equations in vacuum and with perfect fluid source. Many delicate calculations and expressions are given in details so as to address, in a forthcoming work, the issue of global resolution of the characteristic initial value problem for the EYMH system. The method obviously applies to the Einstein–Maxwell and the Einstein-scalar field models as well.

On the spherically symmetric Einstein–Yang–Mills–Higgs equations in Bondi coordinates

We revisit and generalize, to the Einstein–Yang–Mills–Higgs (EYMH) system, previous results of Christodoulou and Chae concerning global solutions for the Einstein-scalar field and the Einstein–Maxwell–Higgs (EMH) equations. The novelty of the present work is twofold. For one thing, the assumption on the self-interaction potential is improved. For another thing, explanation is furnished why the solutions obtained here and those proved by Chae for the EMH system decay more slowly than those established by Christodoulou in the case of self-gravitating scalar fields. Actually, this latter phenomenon stems from the non-vanishing local charge in EMH and EYMH models.

Gravitating BPS monopoles in all d = 4p spacetime dimensions

We have constructed, numerically, both regular and black hole static solutions to the simplest possible gravitating Yang–Mills–Higgs (YMH) systems in 4p spacetime dimensions. The YMH systems consist of 2p th power curvature fields without a Higgs potential. The gravitational systems consist of the ‘Ricci scalar’ of the pth power of the Riemann curvature. In 4 spacetime dimensions this is the usual Einstein–YMH (EYMH) system studied in [1, 2], whose qualitative results we emulate exactly.

Effective metrics in the non-minimal Einstein–Yang–Mills–Higgs theory

We formulate a self-consistent non-minimal five-parameter Einstein–Yang–Mills–Higgs (EYMH) model and analyse it in terms of effective (associated, color and color-acoustic) metrics. We use a formalism of constitutive tensors in order to reformulate master equations for the gauge, scalar and gravitational fields and reconstruct in the algebraic manner the so-called associated metrics for the Yang–Mills field. Using WKB-approximation we find color metrics for the Yang–Mills field and color-acoustic metric for the Higgs field in the framework of five-parameter EYMH model. Based on explicit representation of these effective metrics for the EYMH system with uniaxial symmetry, we consider cosmological applications for Bianchi-I, FLRW and de Sitter models. We focus on the analysis of the obtained expressions for velocities of propagation of longitudinal and transversal color and color-acoustic waves in a (quasi)vacuum interacting with curvature; we show that curvature coupling results in time variations of these velocities. We show, that the effective metrics can be regular or can possess singularities depending on the choice of the parameters of non-minimal coupling in the cosmological models under discussion. We consider a physical interpretation of such singularities in terms of phase velocities of color and color-acoustic waves, using the terms “wave stopping” and “trapped surface”.

Non-minimal pp-wave Einstein–Yang–Mills–Higgs model: color cross-effects induced by curvature

Non-minimal interactions in the pp-wave Einstein–Yang–Mills–Higgs (EYMH) model are shown to give rise to color cross-effects analogous to the magneto-electricity in the Maxwell theory. In order to illustrate the significance of these color cross-effects, we reconstruct the effective (associated, color, and color-acoustic) metrics for the pp-wave non-minimal seven-parameter EYMH model with parallel gauge and scalar background fields. Then these metrics are used as hints for obtaining explicit exact solutions of the non-minimally extended Yang–Mills and Higgs equations for the test fields propagating in the vacuum interacting with curvature. The influence of the non-minimal coupling on the test particle motion is interpreted in terms of the so-called trapped surfaces, introduced in the Analog Gravity theory.

An Existence Proof for the Gravitating BPS Monopole

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. Communicated by Sergiu Klainerman

Spherical symmetry of generalized EYMH fields

The possible actions of symmetry groups on generalized Higgs fields coupled to an Einstein–Yang–Mills field are studied with differential geometrical techniques involving principal and associated bundles. A classification of conjugacy classes of these actions and the form of the corresponding invariant Einstein–Yang–Mills–Higgs (EYMH) fields is obtained and then applied to the case of static spherically symmetric fields over four-dimensional space-time. We identify the representations of the gauge group for which spherically symmetric Higgs fields exist. Then the set of all field equations for the independent functions that describe these fields is analyzed and the corresponding ordinary system of differential equations is derived and shown to be consistent.

Spherically symmetric Einstein–Yang–Mills–Higgs fields for general compact gauge groups

We discuss and classify the Einstein–Yang–Mills–Higgs (EYMH) fields that are invariant under arbitrary actions of a symmetry group by automorphisms on principal bundles with arbitrary compact gauge groups that project onto the isometries of space-time. In particular, we apply this result to the systematic construction of spherically symmetric EYMH fields in this general setting. Physically reasonable boundary conditions at infinity and/or at the center have been shown to considerably restrict the possible Yang–Mills connections. Here we investigate for which representations of the gauge group Higgs fields may be spherically symmetric or may at least contribute to a spherically symmetric stress-energy tensor.

On further generalization of the rigidity theorem for spacetimes with a stationary event horizon or a compact Cauchy horizon

A rigidity theorem that applies to smooth electrovacuum spacetimes which represent either (A) an asymptotically flat stationary black hole or (B) a cosmological spacetime with a compact Cauchy horizon ruled by closed null geodesics was given in a recent paper by Friedrich et al (1999 Commun. Math. Phys. 204 691-707). Here we enlarge the framework of the corresponding investigations by allowing the presence of other types of matter fields. In the first part the matter fields are involved merely implicitly via the assumption that the dominant energy condition is satisfied. In the second part Einstein-Klein-Gordon (EKG), Einstein-[non-Abelian]-Higgs (E[nA]H), Einstein-[Maxwell]-Yang-Mills-dilaton (E[M]YMd) and Einstein-Yang-Mills-Higgs (EYMH) systems are studied. The black hole event horizon or, respectively, the compact Cauchy horizon of the considered spacetimes is assumed to be a smooth non-degenerate null hypersurface. It is proved that there exists a Killing vector field in a one-sided neighbourhood of the horizon in EKG, E[nA]H, E[M]YMd and EYMH spacetimes. This Killing vector field is normal to the horizon, moreover, the associated matter fields are also shown to be invariant with respect to it. The presented results provide generalizations of the rigidity theorems of Hawking (for case A) and of Moncrief and Isenberg (for case B) and, in turn, they strengthen the validity of both the black hole rigidity scenario and the strong cosmic censor conjecture of classical general relativity.