Nonlinear Spinor Field Equations in Gravitational Theory: Spherical Symmetric Soliton-Like Solutions


This paper deals with an extension of a previous work [Gravitation & Cosmology, Vol. 4, 1998, pp 107-113] to exact spherical symmetric solutions to the spinor field equations with nonlinear terms which are arbitrary functions of S=ψψ, taking into account their own gravitational field. Equations with power and polynomial nonlinearities are studied in detail. It is shown that the initial set of the Einstein and spinor field equations with a power nonlinearity has regular solutions with spinor field localized energy and charge densities. The total energy and charge are finite. Besides, exact solutions, including soliton-like solutions, to the spinor field equations are also obtained in flat space-time.

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V. Adanhounme, A. Adomou, F. Codo and M. Hounkonnou, "Nonlinear Spinor Field Equations in Gravitational Theory: Spherical Symmetric Soliton-Like Solutions," Journal of Modern Physics, Vol. 3 No. 9, 2012, pp. 935-942. doi: 10.4236/jmp.2012.39122.

Conflicts of Interest

The authors declare no conflicts of interest.


[1] D. V. Galtsov, Institute of Physics Conference Series, No. 173, 2002, pp. 255-261.
[2] J. Govaerts, “The Quantum Geometer’s Universe: Particles, Interactions and Topology,” Proceedings of the Second International Workshop on Contemporary Problems in Mathematical Physics, Cotonou, 28 October-2 November 2001, pp. 79-212. doi:10.1142/9789812777560_0002
[3] D. Brill and J. Wheeler, “Assessment of Everett’s ‘Relative State’ Formulation of Quantum Theory,” Reviews of Modern Physics, Vol. 29, No. 3, 1957, pp. 463-465. doi:10.1103/RevModPhys.29.465
[4] V. A. Zhelnorovich, “Theory of Spinors and Its Application to Physics and Mechanics,” Nauka, Moscow, 1982.
[5] N. N. Bogoliubov and D. V. Shirkov, “Introduction to the Theory of Quantized Fields,” Nauka, Moscou, 1976.
[6] S. Schweber, “Introduction to the Relativistic Quantum Field Theory,” Harper & Row, Cop., New York, 1961.
[7] A. Adomou, R. Alvarado and G. N. Shikin, Izvestiya Vuzov, Fizika, Vol. 8, 1995, pp. 63-68.
[8] A. Adomou and G. N. Shikin, Gravitation & Cosmology, Vol. 4, No. 2, 1998, pp. 107-113.
[9] G. N. Shikin, “Nonlinear Fields in Theory of Gravitation,” Moscow, 1995.
[10] A. O. Barut and I. H. Duru, Physical Review D, Vol. 36, 1987, p. 3705. doi:10.1103/PhysRevD.36.3705
[11] G. V. Shishkin and V. M. Villalba, “Dirac Equation in External Vector Fields: Separation of Variables,” Journal of Mathematical Physics, Vol. 30, No. 9, 1989, pp. 2132-2142. doi:10.1063/1.528215
[12] G. V. Shishkin and I. E. Andrushkevich, “Criteria of Separability of the Variables in the Dirac Equation in Gravitational Fields,” Theoretical and Mathematical Physics, Vol. 70, No. 2, 1987, pp. 204-214. doi:10.1007/BF01039211
[13] M. N. Hounkonnou and J. E. B. Mendy, “Exact Solutions of the Dirac Equation in a Nonfactorizable Metric,” Journal of Mathematical Physics, Vol. 40, No. 8, 1999, pp. 3827-3842. doi:10.1063/1.532928
[14] C. W. Misner, K. S. Thorne and J. A. Wheeler, “Gravitation,” Freedman, San Francisco, 1973.

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