Nonlinear spinor field equations in gravitational theory: spherical symmetric soliton-like solutions

TL;DR

This paper extends previous work to find exact spherical symmetric solutions to nonlinear spinor field equations coupled with gravity, demonstrating regular, localized energy and charge densities, including soliton-like solutions in flat spacetime.

Contribution

It provides new exact solutions to nonlinear spinor-gravity equations, including soliton-like configurations, with detailed analysis of power and polynomial nonlinearities.

Findings

Solutions have finite total energy and charge.

Regular localized energy densities are achieved.

Includes soliton-like solutions in flat spacetime.

Abstract

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=\bar{\psi}\psi $, 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.