Blow-up for solutions of hyperbolic PDE and spacetime singularities

Details Blow-up for solutions of hyperbolic PDE and spacetime singularities Blow-up for solutions of hyperbolic PDE and spacetime singularities

2000-06-16

arxiv.org/abs/gr-qc/0006060v1

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

Contribution to proceedings of Journees EDP Atlantique

Scientific paper

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.

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