Blow-up for solutions of hyperbolic PDE and spacetime singularities

Alan D. Rendall

Journées équations aux dérivées partielles (2000)

  • page 1-12
  • ISSN: 0752-0360

Abstract

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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 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.

How to cite

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Rendall, Alan D.. "Blow-up for solutions of hyperbolic PDE and spacetime singularities." Journées équations aux dérivées partielles (2000): 1-12. <http://eudml.org/doc/93391>.

@article{Rendall2000,
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.},
author = {Rendall, Alan D.},
journal = {Journées équations aux dérivées partielles},
keywords = {nonlinear hyperbolic systems},
language = {eng},
pages = {1-12},
publisher = {Université de Nantes},
title = {Blow-up for solutions of hyperbolic PDE and spacetime singularities},
url = {http://eudml.org/doc/93391},
year = {2000},
}

TY - JOUR
AU - Rendall, Alan D.
TI - Blow-up for solutions of hyperbolic PDE and spacetime singularities
JO - Journées équations aux dérivées partielles
PY - 2000
PB - Université de Nantes
SP - 1
EP - 12
AB - 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.
LA - eng
KW - nonlinear hyperbolic systems
UR - http://eudml.org/doc/93391
ER -

References

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