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

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, 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.

Perturbing the ground state of Dirac stars

“…In this section we review static solutions. Static solutions were first found in [1] and have been studied by various authors [18,[20][21][22][25][26][27][28]. By static we mean only that the spacetime is time-independent (the matter fields may retain a time-dependence).…”

“…Dynamical solutions of the Einstein-Dirac system [23,24] were initiated by Ventrella and Choptuik [23] in a study of type II critical collapse. More recently a comparison of the space of static solutions for boson, Dirac, and Proca stars was given in [18,25], Dirac star solutions in which the fermions have interactions were found in [26][27][28], and for the first time spinning Dirac stars were solved for in [29].…”

Plane Symmetric Solutions to the Nonlinear Spinor Field Equations in General Relativity Theory

“…V. Adanhoum, A. Adomou, F. P. Codo and M. N. Hounkonnou have obtained spherical-symmetric soliton-like solutions of nonlinear spinor field equations in gravitational theory. The regularity properties of the obtained solutions as well as the asymptotic behavior of the energy and charge densities are studied [4].…”

Test of Einstein's Mass-Energy Relation

“…As a matter of fact, this relation is related with a number of fundamental problems in physics, such as the relationship between quantum mechanics and classical one, the self-potentials of an elementary particles, the Lorentz transformation law for different parameters and Lorentz violation, the structure of the space-time etc. The main purpose of this letter is to draw the attention of physical society towards this problem.The Dirac equation with different potentials describes elementary particles, and maybe give some explanations for dark matter and dark energy (Gu, 2007a;Gu, 2008;Gu, 2017;Adanhounme, Adomou, Codo, & Hounkonnou, 2012;Ribas, Devecchi, & Kremer, 2005;de Vega, 2007;Vacaru, 2015). For spinors with self-potentials such as nonlinear potential and electromagnetic one A µ , detailed calculation shows the potentials result in different energy-speed relations, which can be used as fingerprints of the interactions.…”

“…The Dirac equation with different potentials describes elementary particles, and maybe give some explanations for dark matter and dark energy (Gu, 2007a;Gu, 2008;Gu, 2017;Adanhounme, Adomou, Codo, & Hounkonnou, 2012;Ribas, Devecchi, & Kremer, 2005;de Vega, 2007;Vacaru, 2015). For spinors with self-potentials such as nonlinear potential and electromagnetic one A µ , detailed calculation shows the potentials result in different energy-speed relations, which can be used as fingerprints of the interactions.…”