Particle-like solutions of the Einstein–Dirac–Maxwell equations

Particle-Like Solutions of the Einstein-Dirac-Maxwell Equations

We consider the coupled Einstein-Dirac-Maxwell equations for a static, spherically symmetric system of two fermions in a singlet spinor state. Soliton-like solutions are constructed numerically. The stability and the properties of the ground state solutions are discussed for different values of the electromagnetic coupling constant. We find solutions even when the electromagnetic coupling is so...

Particle-Like Solutions of the Einstein-Dirac Equations

The coupled Einstein-Dirac equations for a static, spherically symmetric system of two fermions in a singlet spinor state are derived. Using numerical methods, we construct an infinite number of soliton-like solutions of these equations. The stability of the solutions is analyzed. For weak coupling (i.e., small rest mass of the fermions), all the solutions are linearly stable (with respect to s...

Exact solutions for wave-like equations by differential transform method

Differential transform method has been applied to solve many functional equations so far. In this article, we have used this method to solve wave-like equations. Differential transform method is capable of reducing the size of computational work. Exact solutions can also be achieved by the known forms of the series solutions. Some examples are prepared to show theefficiency and simplicity of th...

Perturbation Method for Particle-like Solutions of the Einstein-Dirac Equations

Perturbation Method for Particle-like Solutions of the Einstein-dirac-maxwell Equations

The aim of this Note is to prove by a perturbation method the existence of solutions of the coupled Einstein-Dirac-Maxwell equations for a static, spherically symmetric system of two fermions in a singlet spinor state and with the electromagnetic coupling constant ` e m ́ 2 < 1. We show that the nondegenerate solution of Choquard’s equation generates a branch of solutions of the Einstein-Dirac-M...