PL EN


Preferencje help
Widoczny [Schowaj] Abstrakt
Liczba wyników
1997 | 41 | 1 | 119-131
Tytuł artykułu

Well posed reduced systems for the Einstein equations

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
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.
Słowa kluczowe
Rocznik
Tom
41
Numer
1
Strony
119-131
Opis fizyczny
Daty
wydano
1997
Twórcy
  • Gravitation et Cosmologie Relativiste, Université de Paris VI, t.22-12, 75252 Paris, France
  • Department of Physics and Astronomy, University of North Carolina, Chapel Hill, NC 27599-3255, U.S.A.
Bibliografia
  • [1] A. Abrahams, A. Anderson, Y. Choquet-Bruhat and J. W. York, Einstein and Yang-Mills theories in hyperbolic form without gauge fixing, Phys. Rev. Letters 75 (1995), 3377-3381.
  • [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.
  • [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.
  • [4] L. Bel, C.R. Acad. Sci. Paris 246 (1958), 3105.
  • [5] C. Bona, J. Masso, E. Seidel and J. Stela, A new formalism for numerical relativity, Phys. Rev. Letters 75 (1995), 600-603.
  • [6] Y. Choquet (Foures)-Bruhat, Sur L'Intégration des Équations de la Relativité Générale, J. Rat. Mechanics and Anal. 5 (1956), 951-966.
  • [7] Y. Choquet-Bruhat and D. Christodoulou, Elliptic systems in $H_s,δ$ spaces on manifolds which are Euclidean at infinity,Acta. Math. 146 (1981), 129-150.
  • [8] Y. Choquet-Bruhat and T. Ruggeri, Hyperbolicity of the 3+1 system of Einstein equations, Commun. Math. Phys. 89 (1983), 269-275.
  • [9] Y. Choquet-Bruhat and J. W. York, The Cauchy problem in: General Relativity and Gravitation, A. Held (ed.), Plenum, New York, 1980, 99-172.
  • [10] Y. Choquet-Bruhat and J. W. York, Geometrical well posed systems for the Einstein equations, C.R. Acad. Sci. Paris 321 (1995), Série I, 1089-1095.
  • [11] Y. Choquet-Bruhat and J. W. York, Mixed Elliptic and Hyperbolic Systems for the Einstein Equations, in: Gravitation, Electromagnetism and Geometric Structures, G. Ferrarese (ed.) Pythagora Editrice, Bologna, Italy, 1996, 55-73.
  • [12] D. Christodoulou and S. Klainerman, The Global Nonlinear Stability of the Minkowski Space, Princeton University Press, Princeton, 1993.
  • [13] H. Friedrich, Hyperbolic reductions for Einstein's equations, Class. Quantum Grav. 13 (1996), 1451-1459.
  • [14] S. Frittelli and O. Reula, On the Newtonian limit of general relativity, Commun. Math. Phys. 166 (1994), 221-235.
  • [15] C. Lanczos, A remarkable property of the Riemann-Christoffel tensor in four dimensions, Ann. of Math. 39 (1938), 842-850.
  • [16] J. Leray, Hyperbolic Differential Equations, Institute for Advanced Study, Princeton, 1952.
  • [17] J. Leray and Y. Ohya, Équations et systèmes non-linéaires, hyperboliques non-stricts, Math. Ann. 170 (1967), 167-205.
  • [18] A. Lichnerowicz, Problèmes globaux en Mécanique Relativiste, Hermann, Paris, 1939.
  • [19] J. W. York, Kinematics and dynamics of general relativity, in: Sources of Gravitaional Radiation, L. Smarr (ed.), Cambridge University Press, Cambridge, 1979, 83-126.
  • [20] J. W. York, Bel-Robinson Gravitational Superenergy and Flatness, in: Gravitation and Geometry, W. Rindler and A. Trautman (eds.), Bibliopolis, Naples, Italy, 1987, 497-505.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-bcpv41z1p119bwm
JavaScript jest wyłączony w Twojej przeglądarce internetowej. Włącz go, a następnie odśwież stronę, aby móc w pełni z niej korzystać.