Abstract
The present research work deals with an extension of a previous work entitled [Exact Soliton-like spherical symmetric solutions of the Heisenberg-Ivanenko type nonlinear spinor field equation in gravitational theory, Journal of Applied Mathematics and Physics, 2020, 8, 1236-1254] to Analytical Soliton-Like Solutions to Nonlinear Dirac Equation of Spinor Field in Spherical Symmetric Metric. The nonlinear terms in the Lagrangian density are functions of the invariant . Equations with power and polynomial nonlinearities are thoroughly scrutinized. It is shown that soliton is responsible for the deformation in the metric and hence in the geometry as well as gravitational field. The role of nonlinearity and the influence of the proper gravitational field of the elementary particles are also examined. The consideration of the nonlinear terms in the spinor Lagrangian, the own gravitational field of elementary particles and the geometrical properties of the metric are necessary and sufficient conditions in order to obtain soliton-like solutions with total charge and total spin in general relativity.
Highlights
IntroductionIn the theory of General Relativity, the structure of elementary particles confi-. J
The present research work deals with an extension of a previous work entitled [Exact Soliton-like spherical symmetric solutions of the Heisenberg-Ivanenko type nonlinear spinor field equation in gravitational theory, Journal of Applied Mathematics and Physics, 2020, 8, 1236-1254] to Analytical Soliton-Like Solutions to Nonlinear Dirac Equation of Spinor Field in Spherical Symmetric Metric
It is shown that soliton is responsible for the deformation in the metric and in the geometry as well as gravitational field
Summary
In the theory of General Relativity, the structure of elementary particles confi-. J. The exact static plane-symmetric soliton-like solutions of the nonlinear spinor field equations are investigated in a series articles [3] [4] [5] In all these activities, the authors emphasized that the energy density T00 is localized and the total energy of the system is bounded. The role of the geometrical symmetries in general relativity is introduced by Katzin, Lavine and Davis in a series of papers [11] [12] [13] [14], appearing between 1969 and 1977 They emphasized that the geometrical of the space-time are expressible through the vanishing of the Lie derivative of certain tensors with respect to a vector.
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