[Une méthode de perturbation pour les solutions localisées des équations d'Einstein–Dirac–Maxwell]
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 . 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 . We show that the nondegenerate solution of Choquard's equation generates a branch of solutions of the Einstein–Dirac–Maxwell equations.
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@article{CRMATH_2010__348_13-14_791_0,
author = {Rota Nodari, Simona},
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},
url = {http://www.numdam.org/articles/10.1016/j.crma.2010.06.003/}
}
TY - JOUR AU - Rota Nodari, Simona 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 UR - http://www.numdam.org/articles/10.1016/j.crma.2010.06.003/ DO - 10.1016/j.crma.2010.06.003 LA - en ID - CRMATH_2010__348_13-14_791_0 ER -
%0 Journal Article %A Rota Nodari, Simona %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 %U http://www.numdam.org/articles/10.1016/j.crma.2010.06.003/ %R 10.1016/j.crma.2010.06.003 %G en %F CRMATH_2010__348_13-14_791_0
Rota Nodari, Simona. Perturbation method for particle-like solutions of the Einstein–Dirac–Maxwell equations. Comptes Rendus. Mathématique, Tome 348 (2010) no. 13-14, pp. 791-794. doi : 10.1016/j.crma.2010.06.003. http://www.numdam.org/articles/10.1016/j.crma.2010.06.003/
[1] Particle-like solutions of the Einstein–Dirac equations, Physical Review D. Particles and Fields. Third Series, Volume 59 (1999), p. 104020
[2] 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] Existence and uniqueness of the minimizing solution of Choquard's nonlinear equation, Studies in Applied Mathematics, Volume 57 (1977), pp. 93-105
[5] The Choquard equation and related questions, Nonlinear Analysis. Theory, Methods and Applications, Volume 4 (1980) no. 6, pp. 1063-1073
[6] Perturbation method for a class of non linear Dirac equations, Differential Integral Equations, Volume 13 (2000) no. 4–6, pp. 707-720
[7] Perturbation method for particle-like solutions of the Einstein–Dirac equations, Ann. Henri Poincaré, Volume 10 (2010) no. 7, pp. 1377-1393 | DOI
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