This work is devoted to the study of Dirac fields and of their evolution on globally hyperbolic asymptotically flat space-times by means of 3+1 decomposition techniques. The principles of the 3+1 decomposition are explained and used to define classes of space-times for which the regularity and fall-off at infinity of the metric are precisely specified. Dirac's equation is expressed and its 3+1 decomposition is described both in terms of Dirac spinors and in the framework of the two-spinor formalism....
We extend the results of a work by L. Hörmander [9] concerning the resolution of the characteristic Cauchy problem for second order wave equations with regular first order potentials. The geometrical background of this work was a spatially compact spacetime with smooth metric. The initial data surface was spacelike or null at each point and merely Lipschitz. We lower the regularity hypotheses on the metric and potential and obtain similar results. The Cauchy problem for a spacelike initial data...
Pour l’équation de Dirac sans masse à l’extérieur d’un trou noir de Kerr lent nous démontrons la complétude asymptotique. Nous introduisons une nouvelle tétrade de Newman-Penrose pour laquelle l’expression de l’équation ne contient pas de termes à longue portée artificiels. La technique principale utilisée est une estimation de Mourre. La géométrie proche de l’horizon exige d’appliquer une transformation unitaire avant de se retrouver dans une situation dans laquelle le générateur de dilatations...
Download Results (CSV)