Self-gravitating Yang monopoles in all dimensions

Physical Review D, 2007

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.

Fortschritte der Physik, 2009

We discuss the construction of non-Abelian black holes and globally regular monopole solutions to N = 2 d = 4 EYM theories. Special emphasis is put on how the attractor mechanism works for the non-Abelian black holes.

Physical Review D - Particles, Fields, Gravitation and Cosmology, 2008

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. 1 in Ref.

Physics Letters B, 2000

We find monopole solutions for a spontaneously broken SU 2 -Higgs system coupled to gravity in asymptotically anti-de Sitter space. We present new analytic and numerical results discussing, in particular, how the gravitational instability of self-gravitating monopoles depends on the value of the cosmological constant. q

Physical Review D, 2001

It is shown that general relativity coupled to nonlinear electrodynamics (NED) with the Lagrangian L(F) , F = Fµν F µν having a correct weak field limit, leads to nontrivial spherically symmetric solutions with a globally regular metric if and only if the electric charge is zero and L(F) tends to a finite limit as F → ∞. Properties and examples of such solutions, which include magnetic black holes and solitonlike objects (monopoles), are discussed. Magnetic solutions are compared with their electric counterparts. A duality between solutions of different theories specified in two alternative formulations of NED (called the F P duality) is used as a tool for this comparison.

Soviet Physics Journal, 1982

2021

Using numerical algebra tools, new classes of monopole solutions are obtained to the static, spherically-symmetric vacuum field equations of five-dimensional general relativity. First proposed by Kaluza, 5D general relativity unites gravity and classical electromagnetism with a scalar field. These monopoles correspond to bodies carrying mass, electric charge, and scalar charge. The Reissner-Nordström limit allows us to constrain the signature of the fifth component to be spacelike, but valid solutions are obtained for either sign of the scalar field. We find that Kaluza vacuum solutions imply the scalar field energy density is the negative of the electric field energy density, so the total electric and scalar field energy of the monopole is zero. Yet the new solutions provide reasonable Reissner-Nordström and Coulomb limits in mathematical form, with varying possibilities for the scalar field. The vanishing of the total electric and scalar field energy density for vacuum solutions seems to imply the scalar field can be understood as a negative-energy foundation on which the electric field is built. R ab = 0 (1) where R ab is the 5D Ricci tensor. We consider in particular time-independent vacuum solutions in spherical symmetry. The radial coordinate r is the only variable for the gravitational, electromagnetic, and scalar fields. The central object is presumed to carry mass, electric charge, and scalar charge. Each of these 3 charges corresponds to the integration constant for each of the 3 field equations: gravitational, electromagnetic, and scalar. There is a wide body of literature regarding static, spherically-symmetric solutions to the classical vacuum Kaluza field equations (1). These solutions are variously known as "1-bodies", "monopoles" or " solitons". They fall into the two classes of neutral or electrically-charged. Mass (gravitational charge) and scalar charge are expected in both cases. These solutions invite comparison with the standard Reissner-Nordström (R-N) solution of general relativity, which gives the gravitational field of an electrically-charged object. For a neutral object, the point of comparison is the Schwarzschild solution. Generally speaking the time-time component g tt of the 5D metric will depend on the mass M , the component g t5 will depend on the electric charge Q, and the component g 55 will depend on the scalar charge S. The other diagonal components of g ab corresponding to angular variables are non-zero, and all other off-diagonal components are zero. Chodos & Detweiler [4] investigated the 5D vacuum equations (1), but they also obtained a general class of exact solutions to the 5D field equations with sources, and investigated their weak-field limit. They noted that for a particular value of the scalar charge S, the scalar field effects would vanish and the Reissner-Nordström limit is recovered. Yet the R-N limit is difficult to discern in their solutions, and the separate contributions of gravitational and electromagnetic energy cannot be distinguished in their general solution. Sorkin [5] obtained a solution to (1) he called the "Kaluza-Klein monopole". It was assumed that the fifth dimension is spacelike, microscopic, and compact, with a new ad hoc lengthscale representing the size of this dimension as proposed by Klein[3]. A 5D vacuum solution was identified by applying a procedure to a known 4D metric. It had electromagnetic behavior, but no electric field. The Sorkin solution allowed a 4D radial coordinate, instead of the usual 3D Schwarzschild-type radial coordinate, and the near-field behavior of the solution does not correspond to a R-N limit. Sorkin called his solution a "soliton". The mass and charge of the soliton were proposed, but it had some curious properties. One conclusion was that some theorems developed for 4D solutions to the Einstein equations may not apply to 5D solutions to (1), and therefore to the 4D projections of those solutions. Gross and Perry [6] obtained a neutral particle solution, so g 5t = 0. Yet they kept an off-diagonal spatial term, g 5φ , which corresponds to the azimuthal component of the magnetic vector potential, A ϕ. This provided a radial component to the magnetic field, and was identified as a magnetic monopole solution. Since no magnetic monopoles are found in nature, we consider such solutions unphysical, and therefore expect the static Kaluza monopoles to involve electric charge and to create an electric field. Davidson and Owen [7] obtained a neutral-body solution to (1), with a diagonal and isotropic g ab. Their solution had a Schwarzschild near-field limit for the g tt component of the 4D metric, but the spatial isotropic components did not abide the usual Schwarzschild form in isotropic coordinates. The fifth coordinate was stated to be compact and microscopic, with a characteristic radius, but in effect the classical equations under the cylinder condition were solved. Ref. [7] obtained an expression for the mass from an effective energy momentum tensor implied by the solution, under the assumption that the effective metric g ef f µν = g 55 g µν , otherwise known as a conformal transformation of the metric. The resultant effective mass density was given as a powerlaw in the radial coordinate r, whose leading term is ∝ (2/a) 1 − p 2 /r 4 , where a and p are free constants. The effective mass is seen to be a difference of terms, and the two terms are identified as two types of mass. Both fall off like 1/r 2. It was speculated that the second mass was associated with electric charge, but a neutral solution was under consideration. The most natural explanation seems to us, rather, to be that there are two contributions to the gravitating mass-energy: the central mass and its associated scalar field. That is the interpretation pursued in this article. In a follow-up work, Davison & Owen [8] repeated their previous calculation [7], but now considered a rotation of the diagonal solution between the time coordinate and the x 5 coordinate. This introduces an off-diagonal term in the 5D metric which they identified with electric charge. However, they introduced a new free parameter into their

2005

Multidimensional configurations with a Minkowski external spacetime and a spherically symmetric global monopole in extra dimensions are discussed in the context of the braneworld concept. The monopole is formed with a hedgehoglike set of scalar fields φ i with a symmetry-breaking potential V depending on the magnitude φ 2 = φ i φ i . All possible kinds of globally regular configurations are singled out without specifying the shape of V ( φ ). These variants are governed by the maximum value φ m of the scalar field, characterizing the energy scale of symmetry breaking. If φ m < φ cr (where φ cr is a critical value of φ related to the multidimensional Planck scale), the monopole reaches infinite radii, whereas in the "strong field regime," when φ m ≥ φ cr , the monopole may end with a finite-radius cylinder or have two regular centers. The warp factors of monopoles with both infinite and finite radii may either exponentially grow or tend to finite constant values far from the center. All such configurations are shown to be able to trap test scalar matter, in striking contrast to RS2 type five-dimensional models. The monopole structures obtained analytically are also found numerically for the Mexican hat potential with an additional parameter acting as a cosmological constant.

Physics Letters B, 1999

We consider monopole and dyon classical solutions of the Yang-Mills-Higgs system coupled to gravity in asymptotically anti-de Sitter space. We discuss both singular and regular solutions to the second order equations of motion showing that singular Wu-Yang like dyons can be found, the resulting metric being of the Reissner-Nördstrom type (with cosmological constant). Concerning regular solutions, we analyze the conditions under which they can be constructed discussing, for vanishing coupling constant, the main distinctive features related to the anti-de Sitter asymptotic condition; in particular, we find in this case that the v.e.v. of the Higgs scalar, | H(∞)|, should be quantized in units of the natural mass scale 1/e r 0 (related to the cosmological constant) according to | H(∞)| 2 = m(m + 1)(e r 0 ) −2 , with m ∈ Z.

International Journal of Modern Physics, 2019

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