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

TL;DR

This paper proves the existence of static, spherically symmetric solutions to the Einstein-Dirac-Maxwell equations for two fermions using a perturbation method, linking solutions to Choquard's equation.

Contribution

It introduces a perturbation approach to establish solutions for Einstein-Dirac-Maxwell equations, connecting them to solutions of Choquard's equation.

Findings

Existence of solutions for the coupled equations under specified conditions.

Solutions form a branch generated by Choquard's equation.

Applicable to systems with electromagnetic coupling constant less than one.

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.