Plane Symmetric Solutions to the Nonlinear Spinor Field Equations in General Relativity Theory

Adomou, A.; Edou, Jonas; Massou, Siaka

doi:10.4236/jmp.2019.1010081

Cited by 9 publications

(12 citation statements)

References 9 publications

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“…As defines in [4], the general form of the spin tensor for the spinor field is { } Note from (135) that the spin tensor of the spinor field has a finite value.…”

Section: Resultsmentioning

confidence: 99%

Soliton-Like Spherical Symmetric Solutions of the Nonlinear Spinor Field Equations Depending on the Invariant Function IP=P2 in the General Relativity Theory

Adomoi¹,

Edou²,

Massou³

2019

JAMP

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The present research work is considered as part II of the previous work entitled [Plane Symmetric Solutions to the Nonlinear Spinor Field Equations in General Relativity Theory, jmp, 2019, 10, 1222-1234]. Here, we opt for the static spherical symmetric metric. In this metric, we have obtained spherical symmetric soliton-like solutions to the spinor field equations with nonlinear terms, which are arbitrary functions of

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“…As defines in [4], the general form of the spin tensor for the spinor field is { } Note from (135) that the spin tensor of the spinor field has a finite value.…”

Section: Resultsmentioning

confidence: 99%

Soliton-Like Spherical Symmetric Solutions of the Nonlinear Spinor Field Equations Depending on the Invariant Function IP=P2 in the General Relativity Theory

Adomoi¹,

Edou²,

Massou³

2019

JAMP

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“…Let us emphasize that the total charge and spin of the self-consistent system of spinor and gravitational field equations are unlimited. The divergence of the total charge and spin is related to the non-consideration of the torsion and the properties of the static plane-symmetric utilized [2] [3] [4]. For an excellent review of the interacting scalar and spinor fields in plane-symmetric metric refer to [5] [6] [7].…”

Section: Introductionmentioning

confidence: 99%

Spherical Symmetric Solitons of Interacting Spinor, Scalar and Gravitational Fields in General Relativity

Edou¹,

Adomou²,

Massou³

2021

JHEPGC

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The concept of soliton as regular localized stable solutions of nonlinear differential equations is being widely utilized in pure science for various aims. In present analysis, the soliton concept is used as a model in order to describe the configurations of elementary particles in general relativity. To this end, our study deals with the spherical symmetric solitons of interacting Spinor, Scalar and Gravitational Fields in General Relativity. Thus, exact spherical symmetric general solutions to the interaction of spinor, scalar and gravitational field equations have been obtained. The Einstein equations have been transformed into a Liouville equation type and solved. Let us emphasize that these solutions are regular with localized energy density and finite total energy. In addition, the total charge and spin are limited. Moreover, the obtained solutions are soliton-like solutions. These solutions can be used in order to describe the configurations of elementary particles.

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“…In 1995, G. N. Shikin investigated the basics of soliton concept in General Relativity [1]. In 1998, A. Adomou and G. N. Shikin have obtained exact plane-symmetric solutions to the spinor field equations with nonlinear terms, which are arbitrary functions of the invariant S ψψ = [2]. Five years later, B. Saha and G. N. Shikin studied the system of nonlinear spinor and scalar fields with minimal coupling in general relativity [3].…”

Section: Introductionmentioning

confidence: 99%

Exact Soliton-Like Spherical Symmetric Solutions of the Heisenberg-Ivanenko Type Nonlinear Spinor Field Equation in Gravitational Theory

Adomou¹,

Edou²,

Hontinfinde³

et al. 2020

JAMP

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In the present research work, we have obtained the exact spherical symmetric solutions of Heisenberg-Ivanenko nonlinear spinor field equations in the Gravitational Theory. The nonlinearity in the spinor Lagrangian is given by an arbitrary function which depends on the invariant generated from the bilinear spinor form 2 S I S =. We admit the static spherical symmetric metric. It is shown that a soliton-like configuration has a localized energy density and a finite total energy. In addition, The total charge and total spin are also finite. Role of the metric i.e. the proper gravitational field of elementary particles in the formation of the field configurations with limited total energy, spin and charge has been examined by solving the field equations in flat space-time. It has been established that the obtained solutions are soliton-like configuration with bounded energy density and finite total energy. In order to clarify the role of the nonlinearity in this model, we have obtained exact statical symmetric solutions to the above spinor field equations in the linear case corresponding to Dirac's linear equation. It is proved that soliton-like solutions are absent.

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Plane Symmetric Solutions to the Nonlinear Spinor Field Equations in General Relativity Theory

Abstract: We have obtained exact static plane-symmetric solutions to the spinor field equations with nonlinear terms which are arbitrary functions of invariant

Cited by 9 publications

References 9 publications

Soliton-Like Spherical Symmetric Solutions of the Nonlinear Spinor Field Equations Depending on the Invariant Function <i>I<sub>P</sub></i>=<i>P</i><sup>2</sup> in the General Relativity Theory

Soliton-Like Spherical Symmetric Solutions of the Nonlinear Spinor Field Equations Depending on the Invariant Function <i>I<sub>P</sub></i>=<i>P</i><sup>2</sup> in the General Relativity Theory

Spherical Symmetric Solitons of Interacting Spinor, Scalar and Gravitational Fields in General Relativity

Exact Soliton-Like Spherical Symmetric Solutions of the Heisenberg-Ivanenko Type Nonlinear Spinor Field Equation in Gravitational Theory

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Plane Symmetric Solutions to the Nonlinear Spinor Field Equations in General Relativity Theory

Abstract: We have obtained exact static plane-symmetric solutions to the spinor field equations with nonlinear terms which are arbitrary functions of invariant

Cited by 9 publications

References 9 publications

Soliton-Like Spherical Symmetric Solutions of the Nonlinear Spinor Field Equations Depending on the Invariant Function &lt;i&gt;I&lt;sub&gt;P&lt;/sub&gt;&lt;/i&gt;=&lt;i&gt;P&lt;/i&gt;&lt;sup&gt;2&lt;/sup&gt; in the General Relativity Theory

Soliton-Like Spherical Symmetric Solutions of the Nonlinear Spinor Field Equations Depending on the Invariant Function &lt;i&gt;I&lt;sub&gt;P&lt;/sub&gt;&lt;/i&gt;=&lt;i&gt;P&lt;/i&gt;&lt;sup&gt;2&lt;/sup&gt; in the General Relativity Theory

Spherical Symmetric Solitons of Interacting Spinor, Scalar and Gravitational Fields in General Relativity

Exact Soliton-Like Spherical Symmetric Solutions of the Heisenberg-Ivanenko Type Nonlinear Spinor Field Equation in Gravitational Theory

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Soliton-Like Spherical Symmetric Solutions of the Nonlinear Spinor Field Equations Depending on the Invariant Function <i>I<sub>P</sub></i>=<i>P</i><sup>2</sup> in the General Relativity Theory

Soliton-Like Spherical Symmetric Solutions of the Nonlinear Spinor Field Equations Depending on the Invariant Function <i>I<sub>P</sub></i>=<i>P</i><sup>2</sup> in the General Relativity Theory