Well posed reduced systems for the Einstein equations

Yvonne Choquet-Bruhat; James York

Banach Center Publications (1997)

  • Volume: 41, Issue: 1, page 119-131
  • ISSN: 0137-6934

Abstract

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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.

How to cite

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Choquet-Bruhat, Yvonne, and York, James. "Well posed reduced systems for the Einstein equations." Banach Center Publications 41.1 (1997): 119-131. <http://eudml.org/doc/252237>.

@article{Choquet1997,
abstract = {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.},
author = {Choquet-Bruhat, Yvonne, York, James},
journal = {Banach Center Publications},
keywords = {Einstein equations; hyperbolic differential equations; Cauchy problem},
language = {eng},
number = {1},
pages = {119-131},
title = {Well posed reduced systems for the Einstein equations},
url = {http://eudml.org/doc/252237},
volume = {41},
year = {1997},
}

TY - JOUR
AU - Choquet-Bruhat, Yvonne
AU - York, James
TI - Well posed reduced systems for the Einstein equations
JO - Banach Center Publications
PY - 1997
VL - 41
IS - 1
SP - 119
EP - 131
AB - 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.
LA - eng
KW - Einstein equations; hyperbolic differential equations; Cauchy problem
UR - http://eudml.org/doc/252237
ER -

References

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  2. [2] A. Abrahams, A. Anderson, Y. Choquet-Bruhat and J. W. York, Geometrical hyperbolic systems for general relativity and gauge theories, submitted to Class. Quantum Grav., gr-qc/9605014. Zbl0866.58059
  3. [3] A. Abrahams, A. Anderson, Y. Choquet-Bruhat and J. W. York, A non-strictly hyperbolic system for the Einstein equations with arbitrary lapse and shift, submitted to C.R. Acad. Sci. Paris A. Zbl1020.83503
  4. [4] L. Bel, C.R. Acad. Sci. Paris 246 (1958), 3105. 
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  12. [12] D. Christodoulou and S. Klainerman, The Global Nonlinear Stability of the Minkowski Space, Princeton University Press, Princeton, 1993. Zbl0827.53055
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  17. [17] J. Leray and Y. Ohya, Équations et systèmes non-linéaires, hyperboliques non-stricts, Math. Ann. 170 (1967), 167-205. Zbl0146.33701
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