Comptes Rendus
no. 13-14
Partial Differential Equations
Perturbation method for particle-like solutions of the Einstein–Dirac–Maxwell equations
[Une méthode de perturbation pour les solutions localisées des équations d'Einstein–Dirac–Maxwell]

Présenté par : Haïm Brezis

Simona Rota Nodari1, 2
1 Ceremade (UMR CNRS 7534), Université Paris-Dauphine, place du Maréchal de Lattre de Tassigny, 75775 Paris cedex 16, France
2 Dipartimento di Matematica, Università degli Studi di Milano, Via Saldini 50, 20133 Milano, Italy
Comptes Rendus. Mathématique, Volume 348 (2010) no. 13-14, pp. 791-794.

Le but de cette Note est de démontrer par une méthode de perturbation l'existence de solutions des équations d'Einstein–Dirac–Maxwell pour un système statique, à symétrie sphérique de deux fermions dans un état de singulet et avec une constante de couplage électromagnétique (em)2<1. On montre que la solution non dégénérée de l'équation de Choquard génère une branche de solutions des équations d'Einstein–Dirac–Maxwell.

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 (em)2<1. We show that the nondegenerate solution of Choquard's equation generates a branch of solutions of the Einstein–Dirac–Maxwell equations.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2010.06.003

Simona Rota Nodari 1, 2

1 Ceremade (UMR CNRS 7534), Université Paris-Dauphine, place du Maréchal de Lattre de Tassigny, 75775 Paris cedex 16, France
2 Dipartimento di Matematica, Università degli Studi di Milano, Via Saldini 50, 20133 Milano, Italy 
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Simona Rota Nodari. Perturbation method for particle-like solutions of the Einstein–Dirac–Maxwell equations. Comptes Rendus. Mathématique, Volume 348 (2010) no. 13-14, pp. 791-794. doi : 10.1016/j.crma.2010.06.003. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2010.06.003/

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