Anisotropic cosmological models with nonminimally coupled magnetic field

Balakin, Alexander B.; Zimdahl, Winfried

doi:10.1103/physrevd.71.124014

Cited by 20 publications

(40 citation statements)

References 36 publications

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“…One attempt to realize this idea was made in [7], where the approach based on the symmetry of the susceptibility tensor R ikmn (3) is proposed. In [8,9,13,18] special sets of coupling parameters were found, for which the metric functions of non-minimally coupled systems happened to be regular, and the absence of singularity became one of the arguments for the non-minimal extension of the Einstein-Maxwell theory.…”

Section: Discussionmentioning

confidence: 99%

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Nonminimal monopoles of the Dirac type as realization of the censorship conjecture

2009

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We discuss a class of exact solutions of a three-parameter non-minimally extended EinsteinMaxwell model, which are attributed to non-minimal magnetic monopoles of the Dirac type. We focus on the investigation of the gravitational field of Dirac monopoles for those models, for which the singularity at the central point is hidden inside of an event horizon independently on the mass and charge of the object. We obtained the relationships between the non-minimal coupling constants, for which this requirement is satisfied. As explicit examples, we consider in detail two one-parameter models: first, non-minimally extended Reissner-Nordström model (for the magnetically charged monopole), second, the Drummond-Hathrell model.

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Section: Discussionmentioning

confidence: 99%

“…When q 1 vanishes we take the equation (20) instead of (18), and exponential function exp{κ(4q 2 + q 3 )/4r 4 } instead of (1 + κ|q 1 |/r 4 ) β . The procedure for obtaining the basic inequalities is similar to the one used in the previous case, and it yields the same inequalities (25).…”

Section: Conditions For the Absence Of Naked Singularitymentioning

confidence: 99%

Nonminimal monopoles of the Dirac type as realization of the censorship conjecture

2009

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“…Now, after choosing a model, specified by q and by the relations between q 1 , q 2 , and q 3 , it is important to study exact solutions. Exact solutions of the equations of nonminimal electrodynamics in nonlinear gravitational wave backgrounds were obtained in [10 -14], and a nonminimal Bianchi-I cosmological solution was discussed in [15] in this context. Here we want to study charged black hole and other charged solutions of nonminimal models.…”

Section: Introductionmentioning

confidence: 99%

Nonminimal coupling for the gravitational and electromagnetic fields: Black hole solutions and solitons

Balakin

Bochkarev

Lemos³

2008

Phys. Rev. D

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Using a Lagrangian formalism, a three-parameter nonminimal Einstein-Maxwell theory is established. The three parameters q 1 , q 2 , and q 3 characterize the cross-terms in the Lagrangian, between the Maxwell field and terms linear in the Ricci scalar, Ricci tensor, and Riemann tensor, respectively. Static spherically symmetric equations are set up, and the three parameters are interrelated and chosen so that effectively the system reduces to a one parameter only, q. Specific black hole and other type of one-parameter solutions are studied. First, as a preparation, the Reissner-Nordström solution, with q 1 q 2 q 3 0, is displayed. Then, we search for solutions in which the electric field is regular everywhere as well as asymptotically Coulombian, and the metric potentials are regular at the center as well as asymptotically flat. In this context, the one-parameter model with q 1 ÿq, q 2 2q, q 3 ÿq, called the Gauss-Bonnet model, is analyzed in detail. The study is done through the solution of the Abel equation (the key equation), and the dynamical system associated with the model. There is extra focus on an exact solution of the model and its critical properties. Finally, an exactly integrable one-parameter model, with q 1 ÿq, q 2 q, q 3 0, is considered also in detail. A special submodel, in which the Fibonacci number appears naturally, of this one-parameter model is shown, and the corresponding exact solution is presented. Interestingly enough, it is a soliton of the theory, the Fibonacci soliton, without horizons and with a mild conical singularity at the center.

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“…Let us extract from [61] one of the exact solutions of the non-minimally extended Bianchi-I model with magnetic field (Φ = 0). This solution is characterized by the following features.…”

Section: Exactly Integrable Examplementioning

confidence: 99%

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

2008

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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".

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Anisotropic cosmological models with nonminimally coupled magnetic field

Cited by 20 publications

References 36 publications

Nonminimal monopoles of the Dirac type as realization of the censorship conjecture

Nonminimal monopoles of the Dirac type as realization of the censorship conjecture

Nonminimal coupling for the gravitational and electromagnetic fields: Black hole solutions and solitons

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

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