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

Abstract

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 $(\frac{e}{m}{)}^2<1$. We show that the nondegenerate solution of Choquard's equation generates a branch of solutions of the Einstein-Dirac-Maxwell equations.