Heisenberg-Ivanenko Nonlinear Spinor Field Equation: Spherical Symmetric Soliton-Like Solutions in Gravitational Theory

This research work deals with the concept of soliton as regular localized stable solutions of nonlinear di erential equations. In this context, exact static, spherically symmetric solutions to Heisenberg-Ivanenko nonlinear spinor field equation have been obtained in General Relativity. We opted to the static spherical symmetric metric defined in the pseudoriemannian varieties. It has been shown that the obtained solutions are regular with localized energy density and a finite total energy. In addition, the total charge and the total spin are bounded. Therefore the obtained solutions of Heisenberg-Ivanenko nonlinear spinor field equation are soliton-like configurations. Note that the e ect of gravitational field on the properties of regular localized solutions significantly depends on the symmetry of the system.