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A stable class of spacetimes with naked singularities

Marcus Kriele (1997)

Banach Center Publications

We present a stable class of spacetimes which satisfy the conditions of the singularity theorem of Hawking & Penrose (1970), and which contain naked singularities. This offers counterexamples to a geometric version of the strong cosmic censorship hypothesis.

Algebro-geometric approach to the Ernst equation I. Mathematical Preliminaries

O. Richter, C. Klein (1997)

Banach Center Publications

1. Introduction. It is well known that methods of algebraic geometry and, in particular, Riemann surface techniques are well suited for the solution of nonlinear integrable equations. For instance, for nonlinear evolution equations, so called 'finite gap' solutions have been found by the help of these methods. In 1989 Korotkin [9] succeeded in applying these techniques to the Ernst equation, which is equivalent to Einstein's vacuum equation for axisymmetric stationary fields. But, the Ernst equation...

Blow-up for solutions of hyperbolic PDE and spacetime singularities

Alan D. Rendall (2000)

Journées équations aux dérivées partielles

An important question in mathematical relativity theory is that of the nature of spacetime singularities. The equations of general relativity, the Einstein equations, are essentially hyperbolic in nature and the study of spacetime singularities is naturally related to blow-up phenomena for nonlinear hyperbolic systems. These connections are explained and recent progress in applying the theory of hyperbolic equations in this field is presented. A direction which has turned out to be fruitful is that...

Complétude asymptotique pour l'équation des ondes dans une classe d'espaces-temps stationnaires et asymptotiquement plats

Dietrich Häfner (2001)

Annales de l’institut Fourier

En utilisant une méthode dépendante du temps, nous démontrons la complétude asymptotique pour l'équation des ondes dans une classe d'espaces-temps stationnaires et asymptotiquement plats. On introduit l'observable de vitesse asymptotique et on décrit son spectre (sous des hypothèses plus faibles que pour la complétude asymptotique). Les méthodes utilisées sont inspirées par celles de l'analyse du problème à deux corps en mécanique quantique.

Formulazione intrinseca del problema di Cauchy in relatività generale

Giorgio Ferrarese (1988)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

Viene stabilita una formulazione intrinseca del problema di Cauchy in Relatività generale, per uno spazio-tempo riemanniano descritto da un mezzo continuo globale e non-polare. In termini di variabili proprie: metrica, velocità angolare e di deformazione, densità di pura materia, flusso termico e temperatura. Vengono altresì precisate le condizioni iniziali per i dati di Cauchy su una assegnata superficie spaziale σ 3 ; condizioni in involuzione nel senso d'E. Cartan, le quali mettono in evidenza,...

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