Author(s)

A. Adomou^1,2*, Jonas Edou¹, Siaka Massou¹

¹Department of Theoretical Physics and Mathematics, University of Abomey-Calavi, Abomey-Calavi, Benin.
²National Superior Institute of Industrial Technology, INSTI-Lokossa, National University of Sciences, Technology, Engineer-ing and Mathematics of Abomey, Abomey, Benin.

We have obtained exact static plane-symmetric solutions to the spinor field equations with nonlinear terms which are arbitrary functions of invariant , taking into account their own gravitational field. It is shown that the initial set of the Einstein and spinor field equations with a power-law nonlinearity have regular solutions with a localized energy density of the spinor field only if m=0 (m is the mass parameter in the spinor field equations). Equations with power and polynomial nonlinearities are studied in detail. In this case, a soliton-like configuration has negative energy. We have also obtained exact static plane-symmetric solutions to the above spinor field equations in flat space-time. It is proved that in this case soliton-like solutions are absent.

Lagrangian, Static Plane-Symmetric Metric, Field Equations, Energy-Momentum Tensor, Charge Density, Current Vector, Soliton-Like Solution

Adomou, A. , Edou, J. and Massou, S. (2019) Plane Symmetric Solutions to the Nonlinear Spinor Field Equations in General Relativity Theory. Journal of Modern Physics, 10, 1222-1234. doi: 10.4236/jmp.2019.1010081.