Displaying similar documents to “The Cauchy problem for Lorentz metrics with prescribed Ricci curvature”

Cauchy data on a manifold

Yvonne Choquet-Bruhat, Demetrios Christodoulou, Mauro Francaviglia (1978)

Annales de l'I.H.P. Physique théorique

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Well posed reduced systems for the Einstein equations

Yvonne Choquet-Bruhat, James York (1997)

Banach Center Publications

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We review some well posed formulations of the evolution part of the Cauchy problem of General Relativity that we have recently obtained. We include also a new first order symmetric hyperbolic system based directly on the Riemann tensor and the full Bianchi identities. It has only physical characteristics and matter sources can be included. It is completely equivalent to our other system with these properties.

Blow-up for solutions of hyperbolic PDE and spacetime singularities

Alan D. Rendall (2000)

Journées équations aux dérivées partielles

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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...