Exact static spherical symmetric soliton-like solutions to the scalar and electromagnetic nonlinear induction field equations in general relativity

In this paper, we have obtained exact static spherical symmetric soliton-like solutions to the electromagnetic and scalar nonlinear induction field equations taking into account the own gravitational field of the elementary. The results show that the metric tensor functions are regular with localized energy density. Moreover, the total energy of the nonlinear induction fields is bounded and the total charge of elementary particles has a finite value. The importance of the own gravitational field of elementary particles and the role of the nonlinearity of fields in the determination of these solutions have been proved.