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1997 | 41 | 1 | 35-68
Tytuł artykułu

An introduction to the Einstein-Vlasov system

Autorzy
Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
Słowa kluczowe
Rocznik
Tom
41
Numer
1
Strony
35-68
Opis fizyczny
Daty
wydano
1997
Twórcy
  • Max-Planck-Institut für Gravitationsphysik, Schlaatzweg 1, 14473 Potsdam, Germany
Bibliografia
  • [1] S. Alinhac and P. Gérard, Opérateurs pseudo-différentiels et théorème de Nash-Moser, InterEditions, Paris, 1991.
  • [2] R. Bartnik, The mass of an asymptotically flat manifold, Commun. Pure Appl. Math. 34 (1986), 661-693.
  • [3] J. Binney and S. Tremaine, Galactic dynamics, Princeton University Press, Princeton, 1987.
  • [4] G. A. Burnett and A. D. Rendall, Existence of maximal hypersurfaces in some spherically symmetric spacetimes, Class. Quantum Grav. 13 (1996), 111-123.
  • [5] D. Christodoulou, Violation of cosmic censorship in the gravitational collapse of a dust cloud, Commun. Math. Phys. 93 (1984), 171-195.
  • [6] D. Christodoulou, The problem of a self-gravitating scalar field, Commun. Math. Phys. 105 (1986), 337-361.
  • [7] Y. Choquet-Bruhat, Problème de Cauchy pour le système intégro différentiel d'Einstein-Liouville, Ann. Inst. Fourier 21 (1971), 181-201.
  • [8] Y. Choquet-Bruhat and J. York, The Cauchy problem, in: General Relativity and Gravitation, Vol. 1, A. Held (ed.), Plenum, New York, 1980 99-172.
  • [9] R. Courant and D. Hilbert, Methods of Mathematical Physics, Vol. 2, Wiley, New York, 1989.
  • [10] J. Ehlers, Survey of general relativity theory, in: Relativity, Astrophysics and Cosmology, W. Israel (ed.), Reidel, Dordrecht, 1973, 55-89.
  • [11] R. S. Hamilton, The inverse function theorem of Nash and Moser, Bull. Amer. Math. Soc. 7 (1982), 65-222.
  • [12] S. W. Hawking and G. F. R. Ellis, The large-scale structure of space-time, Cambridge University Press, Cambridge, 1973.
  • [13] P.-L. Lions and B. Perthame, Propagation of moments and regularity for the three-dimensional Vlasov-Poisson system, Invent. Math. 105 (1991), 415-430.
  • [14] A. Majda, Compressible fluid flow and systems of conservation laws in several space variables, Springer, New York, 1984.
  • [15] E. Malec and N. Ó Murchadha, Optical scalars and singularity avoidance in spherical spacetimes, Phys. Rev. D50 (1994), 6033-6036.
  • [16] J. E. Marsden and F. J. Tipler, Maximal hypersurfaces and foliations of constant mean curvature in general relativity, Phys. Rep. 66 (1980), 109-139.
  • [17] K. Pfaffelmoser, Global classical solutions of the Vlasov-Poisson system in three dimensions for general initial data, J. Diff. Equations 95 (1992), 281-303.
  • [18] M. Reed and B. Simon, Methods of modern mathematical physics, Academic Press, New York, 1972.
  • [19] G. Rein, Generic global solutions of the relativistic Vlasov-Maxwell system of plasma physics, Commun. Math. Phys. 135 (1990), 41-78.
  • [20] G. Rein and A. D. Rendall, Global existence of solutions of the spherically symmetric Vlasov-Einstein system with small initial data, Commun. Math. Phys. 150 (1992), 561-583. Erratum: Commun. Math. Phys. 176 (1996), 475-478.
  • [21] G. Rein and A. D. Rendall, Global existence of classical solutions to the Vlasov-Poisson system in a three dimensional, cosmological setting, Arch. Rat. Mech. Anal. 126 (1994), 183-201.
  • [22] G. Rein, A. D. Rendall and J. Schaeffer, A regularity theorem for solutions of the spherically symmetric Vlasov-Einstein system, Commun. Math. Phys. 168 (1995), 467-478.
  • [23] A. D. Rendall, On the choice of matter model in general relativity, Approaches to Numerical Relativity, R. d'Inverno (ed.), Cambridge University Press, Cambridge, 1992, 94-102.
  • [24] A. D. Rendall, Cosmic censorship and the Vlasov equation, Class. Quantum Grav. 9 (1992), L99-L104.
  • [25] A. D. Rendall, Crushing singularities in spacetimes with spherical, plane and hyperbolic symmetry, Class. Quantum Grav. 12 (1995), 1517-1533.
  • [26] D. G. Swanson, Plasma Waves, Academic Press, Boston, 1989.
  • [27] S. L. Shapiro and S. A. Teukolsky, Relativistic stellar dynamics on the computer. I. Motivation and numerical method, Astrophys. J. 298 (1985), 34-57.
  • [28] R. M. Wald, General Relativity, Chicago University Press, Chicago, 1984.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-bcpv41z1p35bwm
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