Conformal Scattering of Maxwell Potentials
[Scattering Conforme des Potentiels de Maxwell]
Nicolas, Jean-Philippe1 ; Taujanskas, Grigalius2
1 LMBA, UMR CNRS 6205, University of Brest, 6 avenue Victor Le Gorgeu, 29200 Brest (France)
2 Faculty of Mathematics, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA (United Kingdom)
Annales de l'Institut Fourier, Online first, 68 p.

We construct a complete conformal scattering theory for finite energy Maxwell potentials on a class of curved, asymptotically flat spacetimes with prescribed smoothness of null infinity and a non-zero ADM mass. In order to define the full set of scattering data, we construct a Lorenz-like gauge which makes the field equations hyperbolic and non-singular up to null infinity, and reduces to an intrinsically solvable ODE on null infinity. We develop a method to solve the characteristic Cauchy problem from this scattering data based on a theorem of Hörmander. In the case of Minkowski space, we further investigate an alternative formulation of the scattering theory by using the Morawetz vector field instead of the usual timelike Killing vector field.

Nous construisons une théorie du scattering conforme complète pour les potentiels de Maxwell d’énergie finie sur une famille d’espaces-temps courbes, asymptotiquement plats, de régularité prescriptible à l’infini isotrope et dont la masse ADM n’est pas nulle. Afin de définir précisément les données de scattering, nous construisons une jauge qui rend les équations de Maxwell (décrites en fonction du potentiel) hyperboliques et non singulières jusqu’à l’infini isotrope et qui se réduit à une EDO résoluble de façon intrinsèque à l’infini isotrope. Nous développons une méthode pour résoudre le problème de Cauchy caractéristique à partir des données de scattering en utilisant un théorème de Hörmander. Dans le cas de l’espace-temps de Minkowski, nous étudions en détail une formulation alternative de la théorie du scattering basée sur l’utilisation du champ de vecteurs de Morawetz plutôt que du champ de Killing temporel usuel.

Reçu le :
Révisé le :
Accepté le :
Première publication :
DOI : 10.5802/aif.3733
Classification : 35P25, 35Q75, 35Q61, 83C30, 83C50, 83C60
Keywords: Scattering, massless fields, Maxwell potentials, conformal geometry, asymptotic analysis
Mots-clés : scattering, champs sans masse, potentiels de Maxwell, géométrie conforme, analyse asymptotique

Nicolas, Jean-Philippe 1 ; Taujanskas, Grigalius 2

1 LMBA, UMR CNRS 6205, University of Brest, 6 avenue Victor Le Gorgeu, 29200 Brest (France)
2 Faculty of Mathematics, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA (United Kingdom) 
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Nicolas, Jean-Philippe; Taujanskas, Grigalius. Conformal Scattering of Maxwell Potentials. Annales de l'Institut Fourier, Online first, 68 p.

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