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Blow-up for solutions of hyperbolic PDE and spacetime singularities

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Rendall,  Alan D.
Geometric Analysis and Gravitation, AEI-Golm, MPI for Gravitational Physics, Max Planck Society;

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Citation

Rendall, A. D. (2000). Blow-up for solutions of hyperbolic PDE and spacetime singularities. In N. Depauw, D. Robert, & X. Saint-Raymond (Eds.), Proceedings of Journees "Equations aux Derivees Partielles" (pp. 1-12). Groupement de Recherche 1151 du CNRS.


Cite as: https://hdl.handle.net/11858/00-001M-0000-0013-576D-2
Abstract
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 of constructing large families of solutions of the Einstein equations with singularities of a simple type by solving singular hyperbolic systems. Heuristic considerations indicate, however, that the generic case will be much more complicated and require different techniques.