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

Simona Rota Nodari (1, 2)

1 CEREMADE - CEntre de REcherches en MAthématiques de la DEcision
2 Dipartimento di Matematica "Federico Enriques"

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

Mots clés: Particle-like solutions; Einstein-Dirac-Maxwell equations; perturbation method

Domaines: Equations aux dérivées partielles [math.AP]

Simona Rota Nodari. Perturbation Method for Particle-like Solutions of the Einstein-Dirac-Maxwell Equations. Comptes Rendus. Mathématique, 2010, 348, pp.Pages 791-794. ⟨10.1016/j.crma.2010.06.003⟩. ⟨hal-00442453⟩