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Comptes Rendus Mathématique
Volume 355, n° 2
pages 187-192 (février 2017)
Doi : 10.1016/j.crma.2016.11.018
Received : 16 July 2016 ;  accepted : 3 November 2016
Cauchy problem on a characteristic cone for the Einstein–Vlasov system: (I) The initial data constraints
Problème de Cauchy sur un cône caractéristique pour le système Einstein–Vlasov : (I) contraintes initiales
 

Jean Baptiste Patenou
 Department of Mathematics and Computer Science, Faculty of Science, University of Dschang, P.O. Box. 67, Dschang, Cameroon 

Abstract

In this paper, one considers a Cauchy problem with data on a characteristic cone for the Einstein–Vlasov system in temporal gauge. One highlights gauge-dependent constraints that, supplemented by the standard constraints i.e. the Hamiltonian and the momentum constraints, define the full set of constraints for the considered setting. One studies their global resolution from a suitable choice of some free data, the behavior of the deduced initial data at the vertex of the cone, and the preservation of the gauge.

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Résumé

Dans cet article, on considère le problème de Cauchy caractéristique sur un cône pour le système des équations d'Einstein–Vlasov en jauge temporelle. On met en évidence les contraintes dépendant de la jauge, qui ensemble avec les contraintes hamiltoniennes et impulsionnelles constituent l'ensemble des équations des contraintes pour le cadre considéré. On étudie la résolution globale de ces équations à partir de certaines données indépendantes, le comportement des données initiales ainsi déduites au voisinage du sommet du cône et la préservation de la jauge.

The full text of this article is available in PDF format.


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