Cosmological Einstein-Skyrme solutions with nonvanishing topological charge

Canfora, Fabrizio; Paliathanasis, Andronikos; Taves, Tim; Zanelli, Jorge

doi:10.1103/physrevd.95.065032

Cited by 23 publications

(34 citation statements)

References 52 publications

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“…Solutions (92), (94) are well-known in the context of perfect fluid LFRW cosmologies [63]. The non-linear σ-model Einstein universe (94) was also found in [64]. Similar solutions when a Skyrme term is added to the theory have been discussed recently in [22,28,65] and present different features.…”

Section: Special Case With Adapted 3-geometry: Lfrw Cosmologies and Esupporting

confidence: 57%

Extensions of the generalized hedgehog ansatz for the Einstein-nonlinear σ-model system: black holes with NUT, black strings and time-dependent solutions

Giacomini

Ortaggio

2019

J. High Energ. Phys.

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We consider a class of ansätze for the construction of exact solutions of the Einstein-nonlinear σ-model system with an arbitrary cosmological constant in (3+1) dimensions. Exploiting a geometric interplay between the SU (2) field and Killing vectors of the spacetime reduces the matter field equations to a single scalar equation (identically satisfied in some cases) and simultaneously simplifies Einstein's equations. This is then exemplified over various classes of spacetimes, which allows us to construct stationary black holes with a NUT parameter and uniform black strings, as well as time-dependent solutions such as Robinson-Trautman and Kundt spacetimes, Vaidyatype radiating black holes and certain Bianchi IX cosmologies. In addition to new solutions, some previously known ones are rederived in a more systematic way. to be solved. For this reason, a lot of work has been devoted to numerical studies, cf., e.g., [3][4][5][6][7][8][9][10][11][12][13][14][15] and references therein.Finding exact solutions of the Einstein-nonlinear σ-model or Einstein-Skyrme system is thus not an easy task. Nevertheless, having in mind a specific physical system, the choice of a good ansatz for the matter field and the spacetime metric may reduce the complexity of the problem. A well-known example is given by the hedgehog ansatz in the presence of spherical symmetry, considered in this context (without backreaction) in [3,16] and further used (also with backreaction) in a number of works, see, e.g., [17][18][19] for reviews and more references. A generalizations of the hedgehog ansatz for the Skyrme-Einstein system beyond spherical symmetry has been constructed in [20] and applied to spacetimes which possess plane or hyperbolic symmetry or are stationary and axisymmetric (see [21] for earlier results for the SU (2) nonlinear σ-model). With similar techniques, topologically non-trivial solutions in curved spacetimes have been obtained in [22].In the present paper we construct further extensions of the ansatz used in [20][21][22]. 1 For simplicity, we restrict ourselves to the SU (2) nonlinear σ-model, without the Skyrme term. 2 On the one hand, we will show that certain solutions obtained in various earlier papers can be in derived in a unified, more sistematic way. On the other hand, we will demonstrate that the same method can also be used to construct some new solutions, and further allows one to drop the requirement of spacetime symmetries assumed in previous works (at least under certain circumstances, as we shall explain in the following). This enables one, in particular, to construct time-dependent Robinson-Trautman or Kundt spacetimes [23] sourced by the SU (2) field. In passing, we will additionally observe that some of the proposed ansätze correspond to truncations of the theory which make it effectively equivalent to Einstein gravity coupled to (depending on the concrete ansatz) two axionic fields, a single scalar field or an anisotropic fluid. Some of the obtained solutions can thus be reinterpreted also in those context...

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Section: Special Case With Adapted 3-geometry: Lfrw Cosmologies and Esupporting

confidence: 57%

Extensions of the generalized hedgehog ansatz for the Einstein-nonlinear σ-model system: black holes with NUT, black strings and time-dependent solutions

Giacomini

Ortaggio

2019

J. High Energ. Phys.

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“…To obtain the meronic black hole we study analytic, Meron-type solutions of the Einstein-Yang-Mills field equations, using the hedgehog Ansatz introduced in [30][31][32][33][34][35][36][37][38][39][40][41][42][43][44][45]. The Yang-Mills SU(2) gauge potential is A = λ A, where A is pure gauge.…”

Section: Jhep06(2019)081mentioning

confidence: 99%

“…The group element U ∈ SU(2) that corresponds to the Meron gauge potential (2.9) can be explicitly written using the generalized hedgehog ansatz [30]. It is interesting to note that such an approach (subsequently worked out in [31][32][33][34][35][36][37][38][39][40][41][42][43][44][45]) was originally developed to analyze the Skyrme and Einstein-Skyrme models, but it also works in the case of Yang-Mills and Einstein-Yang-Mills theories with almost no modifications (as one can see comparing [31,39] with [6,45]). This approach is specially designed for situations in which the group element cannot be deformed continuously to the identity.…”

Section: Generalized Hedgehog Ansatzmentioning

confidence: 99%

Meronic Einstein-Yang-Mills black hole in 5D and gravitational spin from isospin effect

Canfora

Gomberoff

et al. 2019

J. High Energ. Phys.

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We construct an analytic black hole solution in SU(2) Einstein-Yang-Mills theory in five dimensions supporting a Meron field. The gauge field is proportional to a pure gauge and has a non-trivial topological charge. The would-be singularity at the Meron core gets shielded from the exterior by the black hole horizon. The metric has only one integration constant, namely, its ADM mass, which is shown to be finite once an appropriate boundary term is added to the action. The thermodynamics is also worked out, and a first-order phase transition, similar to the one occurring in the Reissner-Nordström case is identified. We also show that the solution produces a spin from isospin effect , i.e., even though the theory is constructed out of bosons only, the combined system of a scalar field and this background may become fermionic. More specifically, we study scalar excitations in this purely bosonic background and find that the system describes fermionic degrees of freedom at spatial infinity. Finally, for the asymptotically AdS 5 case, we study its consequences in the context of the AdS/CFT correspondence.

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“…This solution corresponds to the Lorentzian wormhole constructed in [17]. Here, as we can observe from (16) and (18), it is expressed in a gauge where the "lapse" N (r) of the metric is…”

Section: Particular Solutionsmentioning

confidence: 92%

Topologically nontrivial configurations in the 4d Einstein-nonlinear σ -model system

2017

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We construct exact, regular and topologically non-trivial configurations of the coupled Einsteinnonlinear sigma model in (3+1) dimensions. The ansatz for the nonlinear SU (2) field is regular everywhere and circumvents Derrick's theorem because it depends explicitly on time, but in such a way that its energy-momentum tensor is compatible with a stationary metric. Moreover, the SU (2) configuration cannot be continuously deformed to the trivial Pion vacuum as it possesses a non-trivial winding number. We reduce the full coupled 4D Einstein nonlinear sigma model system to a single second order ordinary differential equation. When the cosmological constant vanishes, such master equation can be further reduced to an Abel equation. Two interesting regular solutions correspond to a stationary traversable wormhole (whose only "exotic matter" is a negative cosmological constant) and a (3+1)-dimensional cylinder whose (2+1)-dimensional section is a Lorentzian squashed sphere. The Klein-Gordon equation in these two families of spacetimes can be solved in terms of special functions. The angular equation gives rise to the Jacobi polynomials while the radial equation belongs to the Poschl-Teller family. The solvability of the Poschl-Teller problem implies non-trivial quantization conditions on the parameters of the theory.

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Cosmological Einstein-Skyrme solutions with nonvanishing topological charge

Cited by 23 publications

References 52 publications

Extensions of the generalized hedgehog ansatz for the Einstein-nonlinear σ-model system: black holes with NUT, black strings and time-dependent solutions

Extensions of the generalized hedgehog ansatz for the Einstein-nonlinear σ-model system: black holes with NUT, black strings and time-dependent solutions

Meronic Einstein-Yang-Mills black hole in 5D and gravitational spin from isospin effect

Topologically nontrivial configurations in the 4d Einstein-nonlinear σ -model system

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