Comptes Rendus
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]
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
@article{CRMATH_2010__348_13-14_791_0,
     author = {Simona Rota Nodari},
     title = {Perturbation method for particle-like solutions of the {Einstein{\textendash}Dirac{\textendash}Maxwell} equations},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {791--794},
     publisher = {Elsevier},
     volume = {348},
     number = {13-14},
     year = {2010},
     doi = {10.1016/j.crma.2010.06.003},
     language = {en},
}
TY  - JOUR
AU  - Simona Rota Nodari
TI  - Perturbation method for particle-like solutions of the Einstein–Dirac–Maxwell equations
JO  - Comptes Rendus. Mathématique
PY  - 2010
SP  - 791
EP  - 794
VL  - 348
IS  - 13-14
PB  - Elsevier
DO  - 10.1016/j.crma.2010.06.003
LA  - en
ID  - CRMATH_2010__348_13-14_791_0
ER  - 
%0 Journal Article
%A Simona Rota Nodari
%T Perturbation method for particle-like solutions of the Einstein–Dirac–Maxwell equations
%J Comptes Rendus. Mathématique
%D 2010
%P 791-794
%V 348
%N 13-14
%I Elsevier
%R 10.1016/j.crma.2010.06.003
%G en
%F CRMATH_2010__348_13-14_791_0
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/

[1] F. Finster; J. Smoller; S.T. Yau Particle-like solutions of the Einstein–Dirac equations, Physical Review D. Particles and Fields. Third Series, Volume 59 (1999), p. 104020

[2] F. Finster; J. Smoller; S.T. Yau Particle-like solutions of the Einstein–Dirac–Maxwell equations, Phys. Lett. A, Volume 259 (1999) no. 6, pp. 431-436

[3] E. Lenzmann, Uniqueness of ground states for pseudo-relativistic Hartree equations, preprint, 2008

[4] E.H. Lieb Existence and uniqueness of the minimizing solution of Choquard's nonlinear equation, Studies in Applied Mathematics, Volume 57 (1977), pp. 93-105

[5] P.L. Lions The Choquard equation and related questions, Nonlinear Analysis. Theory, Methods and Applications, Volume 4 (1980) no. 6, pp. 1063-1073

[6] H. Ounaies Perturbation method for a class of non linear Dirac equations, Differential Integral Equations, Volume 13 (2000) no. 4–6, pp. 707-720

[7] S. Rota Nodari Perturbation method for particle-like solutions of the Einstein–Dirac equations, Ann. Henri Poincaré, Volume 10 (2010) no. 7, pp. 1377-1393 | DOI

Cité par Sources :

Commentaires - Politique