Abstract
In this paper, we have used the static spherical symmetric metric. The parameter of the nonlinearity fields is included in the arbitrary function characterizing the interaction between the electromagnetic and scalar fields. Taking into account the own gravitational field of elementary particles, we have obtained exact static spherical symmetric solutions to the electromagnetic and scalar field equations of nonlinear induction. Considering all forms of the solution of Liouville equation, we proved that the metric functions are regular with localized energy density. Moreover, the total energy of the nonlinear induction fields is bounded and the total charge of the elementary particles has a finite value (soliton-like). In the flat space-time, soliton-like solutions exist.
Highlights
In classical physics, elementary particles are considered as material points
Considering all forms of the solution of Liouville equation, we proved that the metric functions are regular with localized energy density
Soliton-like solutions to nonlinear differential field equations are used as models to describe the complex spatial configuration of elementary particles [4] [5]
Summary
Elementary particles are considered as material points. in the Standard Model (SM), the Grand Unification Theories (GUT), the Super Symmetry Super Strings (SUSY), the theory of gravitation is absent [1]. In [19], the authors determined, soliton-like solutions to the nonlinear electromagnetic field equation interacting with the scalar field in the spherical and/or cylindrical symmetric metric in the presence of the own gravitational field of elementary particle by studying only the special case where S (k,ξ ) = ξ. The objective of this research work is to determine the exact static spherical symmetric soliton-like solutions to the electromagnetic and scalar nonlinear induction field equations taking into account the own gravitational field of elementary particles, describing a massless system, considering all forms of the function S (k,ξ ) , using the calibrated invariance function P= ( I ) P0 ( N − λI ) , under the condition λ I < N.
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