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G. N. Shikin

Publications and source records attributed to G. N. Shikin.

16 recordsLinked to original sources
arXiv2010

Electromagnetic field with induced massive term: Case with spinor field

We consider an interacting system of spinor and electromagnetic field, explicitly depending on the electromagnetic potentials, i.e., interaction with broken gauge invariance. The Lagrangian for interaction is chosen in such a way that the electromagnetic field equation acquires an additional term, which in some cases is proportional to the vector potential of the electromagnetic field. This equation can be interpreted as the equation of motion of photon with induced non-trivial rest-mass. This system of interacting spinor and scalar fields is considered within the scope of Bianchi type-I (BI) cosmological model. It is shown that, as a result of interaction the electromagnetic field vanishes at $t \to \infty$ and the isotropization process of the expansion takes place.

gr-qc↗
arXiv2010

Scalar field in cosmology: Potential for isotropization and inflation

The important role of scalar field in cosmology was noticed by a number of authors. Due to the fact that the scalar field possesses zero spin, it was basically considered in isotropic cosmological models. If considered in an anisotropic model, the linear scalar field does not lead to isotropization of expansion process. One needs to introduce scalar field with nonlinear potential for the isotropization process to take place. In this paper the general form of scalar field potentials leading to the asymptotic isotropization in case of Bianchi type-I cosmological model, and inflationary regime in case of isotropic space-time is obtained. In doing so we solved both direct and inverse problem, where by direct problem we mean to find metric functions and scalar field for the given potential, whereas, the inverse problem means to find the potential and scalar field for the given metric function. The scalar field potentials leading to the inflation and isotropization were found both for harmonic and proper synchronic time.

gr-qc↗
arXiv2010

Electromagnetic field with induced massive term: Case with scalar field

We consider an interacting system of massless scalar and electromagnetic field, with the Lagrangian explicitly depending on the electromagnetic potentials, i.e., interaction with broken gauge invariance. The Lagrangian for interaction is chosen in such a way that the electromagnetic field equation acquires an additional term, which in some cases is proportional to the vector potential of the electromagnetic field. This equation can be interpreted as the equation of motion of photon with induced nonzero rest-mass. This system of interacting fields is considered within the scope of Bianchi type-I (BI) cosmological model. It is shown that, as a result of interaction the electromagnetic field vanishes at $t \to \infty$ and the isotropization process of the expansion takes place.

gr-qc↗
arXiv2004

Magneto-dilatonic Bianchi-I cosmology: isotropization and singularity problems

We study the evolution of Bianchi-I space-times filled with a global unidirectional electromagnetic field $F_{mn}$ interacting with a massless scalar dilatonic field according to the law Ψ(ϕ) F^{mn} F_{mn} where Ψ(ϕ) > 0 is an arbitrary function. A qualitative study, among other results, shows that (i) the volume factor always evolves monotonically, (ii) there exist models becoming isotropic at late times and (iii) the expansion generically starts from a singularity but there can be special models starting from a Killing horizon preceded by a static stage. All these features are confirmed for exact solutions found for the usually considered case Ψ= e^{2λϕ}, λ= const. In particular, isotropizing models are found for |λ| > 1/\sqrt{3}. In the special case |λ| = 1, which corresponds to models of string origin, the string metric behaviour is studied and shown to be qualitatively similar to that of the Einstein frame metric.

gr-qc↗
arXiv2003

Self-gravitating stringlike configurations from nonlinear electodynamics

We consider static, cylindrically symmetric configurations in general relativity coupled to nonlinear electrodynamics (NED) with an arbitrary gauge-invariant Lagrangian of the form $L_{em}= Φ(F)$, $F =F_{mn}F^{mn}$. We study electric and magnetic fields with three possible orientations: radial (R), longitudinal (L) and azimuthal (A), and try to find solitonic stringlike solutions, having a regular axis and a flat metric at large $r$, with a possible angular defect. Assuming the function $Φ(F)$ to be regular at small $F$, it is shown that a regular axis is impossible in R-fields if there is a nonzero effective electric charge and in A-fields if there is a nonzero effective electric current along the axis. Solitonic solutions are only possible for purely magnetic R-fields and purely electric A-fields, in cases when $Φ(F)$ tends to a finite limit at large $F$. For both R- and A-fields, the desired large $r$ asymptotic is only possible with a non- Maxwell behaviour of $Φ(F)$ at small $F$. For L-fields, solutions with a regular axis are easily obtained (and can be found by quadratures) whereas a desired large $r$ asymptotic is only possible in an exceptional solution; the latter gives rise to solitonic configurations in case $Φ(F) = \const \cdot \sqrt{F}$. We give an explicit example of such a solution.

gr-qc↗
arXiv2001

Spherically symmetric scalar vacuum: no-go theorems, black holes and solitons

We prove some theorems characterizing the global properties of static, spherically symmetric configurations of a self-gravitating real scalar field in general relativity (GR) in various dimensions, with an arbitrary potential $V$, not necessarily positive-definite. The results are extended to sigma models, scalar-tensor and curvature-nonlinear theories of gravity. We show that the list of all possible types of space-time causal structure in the models under study is the same as for a constant scalar field, namely, Minkowski (or AdS), Schwarzschild, de Sitter and Schwarzschild - de Sitter, and all horizons are simple. In particular, these theories do not admit regular black holes with any asymptotics. Some special features of (2+1)D gravity are revealed. We give examples of two types of asymptotically flat configurations with positive mass in GR, admitted by the above theorems: (i) a black hole with nontrivial ``scalar hair'' and (ii) a particlelike solution with a regular centre; in both cases, the potential $V$ must be at least partly negative. We also discuss the global effects of conformal mappings that connect different theories. Such effects are illustrated for solutions with a conformal scalar field in GR.

gr-qc↗
arXiv2001

Nonlinear Spinor and Scalar Fields in General Relativity

We consider a system of nonlinear spinor and scalar fields with minimal coupling in general relativity. The nonlinearity in the spinor field Lagrangian is given by an arbitrary function of the invariants generated from the bilinear spinor forms $S= {\bar ψ} ψ$ and $P=i {\bar ψ} γ^5 ψ$; the scalar Lagrangian is chosen as an arbitrary function of the scalar invariant $Υ = ϕ_{,α}ϕ^{,α}$, that becomes linear at $Υ \to 0$. The spinor and the scalar fields in question interact with each other by means of a gravitational field which is given by a plane-symmetric metric. Exact plane-symmetric solutions to the gravitational, spinor and scalar field equations have been obtained. Role of gravitational field in the formation of the field configurations with limited total energy, spin and charge has been investigated. Influence of the change of the sign of energy density of the spinor and scalar fields on the properties of the configurations obtained has been examined. It has been established that under the change of the sign of the scalar field energy density the system in question can be realized physically iff the scalar charge does not exceed some critical value. In case of spinor field no such restriction on its parameter occurs. In general it has been shown that the choice of spinor field nonlinearity can lead to the elimination of scalar field contribution to the metric functions, but leaving its contribution to the total energy unaltered. Key words: Nonlinear spinor field (NLSF), nonlinear scalar field, plane-symmetric metric PACS: 03.65.P, 04.20.H

gr-qc↗
arXiv2001

Cylindrically Symmetric Solitons with Nonlinear Self-Gravitating Scalar Fields

Static, cylindrically symmetric solutions to nonlinear scalar-Einstein equations are considered. Regularity conditions on the symmetry axis and flat or string asymptotic conditions are formulated in order to select soliton-like solutions. Some non-existence theorems are proved, in particular, theorems asserting (i) the absence of black-hole and wormhole-like cylindrically symmetric solutions for any static scalar fields minimally coupled to gravity and (ii) the absence of solutions with a regular axis for scalar fields with the Lagrangian $L=F(I)$, $I=ϕ^αϕ_α$, for any function $F(I)$ possessing a correct weak field limit. Exact solutions for scalar fields with an arbitrary potential function $V(ϕ)$ are obtained by quadratures and are expressed in a parametric form in a few ways, where the parameter may be either the coordinate $x$, or the $ϕ$ field, or one of the metric coefficients. Soliton-like solutions are shown to exist only with $V(ϕ)$ having a variable sign. Some explicit examples of solutions (including a soliton-like one) and their flat-space limit are discussed.}

gr-qc↗
arXiv1999

Kink-like Configurations of Interacting Scalar, Electromagnetic, and Gravitational Fields

We have obtained exact kink-like static plane-symmetric solutions to the self-consistent system of electromagnetic, scalar, and gravitational field equations. It was shown that under certain choice of the interaction Lagrangian the solutions are regular and have localized energy. The linearized instability of corresponding solutions was established both for the case of flat space-time and that of interaction with the proper gravitational field.

math-ph↗
arXiv1996

Exact Self-consistent Particle-like Solutions to the Equations of Nonlinear Scalar Electrodynamics in General Relativity

Exact self-consistent particle-like solutions with spherical and/or cylindrical symmetry to the equations governing the interacting system of scalar, electromagnetic and gravitational fields have been obtained. As a particular case it is shown that the equations of motion admit a special kind of solutions with sharp boundary known as droplets. For these solutions, the physical fields vanish and the space-time is flat outside of the critical sphere or cylinder. Therefore, the mass and the electric charge of these configurations are zero.

gr-qc↗
arXiv1996

Nonlinear Spinor Field in Bianchi type-I Universe filled with Perfect Fluid: Exact Self-consistent Solutions

Self-consistent solutions to nonlinear spinor field equations in General Relativity have been studied for the case of Bianchi type-I space-time filled with perfect fluid. The initial and the asymptotic behavior of the field functions and the metric one has been thoroughly studied. It should be emphasized the absence of initial singularity for some types of solutions and also the isotropic mode of space-time expansion in some special cases.

gr-qc↗
arXiv1996

Droplets in General Relativity: Exact Self-Consistent Solutions to the Interacting Scalar and Electromagnetic Field Equations

It is shown, for the self-consistent system of scalar, electro-magnetic and gravitational fields in general relativity, that the equations of motion admit a special kind of solutions with spherical or cylindrical symmetry. For these solutions, the physical fields vanish and the space-time is flat outside of the critical sphere or cylinder. Therefore, the mass and the electric charge of these configurations are zero. The principal difference between droplet-like solutions with spherical symmetry and those with cylindrical one has been established. In the first case there exists a possibility of continuous transformation of droplet-like configuration into the solitonian one, when for the second case there is no such a possibility.

gr-qc↗