Dynamics of spatially homogeneous solutions of the Einstein-Vlasov equations which are locally rotationally symmetric

Classical and Quantum Gravity

Volumn 16, Issue 6, 1999, Pages 1705-1726

  Rendall, A D ^a   Tod, K P ^b  

^a ALBERT EINSTEIN INSTITUT   (Germany)

^b UNIVERSITY OF OXFORD   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0033242704     PISSN: 02649381     EISSN: None     Source Type: Journal    
DOI: 10.1088/0264-9381/16/6/305     Document Type: Article

References (20)

1. Abraham R and Robbin J 1967 Transversal Mappings and Flows (New York: Benjamin)
2. Arnold V I and Ilyashenko Yu S 1988 Dynamical Systems I ed D V Anosov and V I Arnold (Berlin: Springer)
3. Belinskii V A, Khalatnikov I M and Lifschitz E M 1982 A general solution of the Einstein equations with a time singularity Adv. Phys. 13 639-67
4. Burnett G A 1991 Incompleteness theorems for the spherically symmetric spacetimes Phys. Rev. D 43 1143-9
5. Dunn K A and Tupper B O J 1980 Type I, II and III spatially homogeneous cosmological models with electromagnetic field Astrophys. J. 235 307-34
6. Ehlers J 1973 Survey of general relativity theory Relativity, Astrophysics and Cosmology ed W Israel (Dordrecht: Reidel)
7. Hartman P 1982 Ordinary Differential Equations (Boston, MA: Birkhäuser)
8. Hewitt C G and Wainwright J 1993 A dynamical systems approach to Bianchi cosmologies: orthogonal models of class B Class. Quantum Grav. 10 99-124
9. Kirchgraber U and Palmer K J 1990 Geometry in the Neighborhood of Invariant Manifolds of Maps and Flows and Linearization (Harlow: Longman)
10. 0 cosmologies Class. Quantum Grav. 12 513-41
11. Lukash V N and Starobinski A A 1974 The isotropization of the cosmological expansion owing to particle production Sov. Phys.-JETP 39 742-7
12. Maartens R and Maharaj S D 1985 Collision-free gases in spatially homogeneous spacetimes J. Math. Phys. 26 2869-80
13. Maartens R and Maharaj S D 1990 Collision-free gases in Bianchi spacetimes Gen. Rel. Grav. 22 595-607
14. Rendall A D 1996 The initial singularity in solutions of the Einstein-Vlasov system of Bianchi type I J. Math. Phys. 37 438-51
15. Rendall A D 1997 An introduction to the Einstein-Vlasov system Banach Centre Publ. 41 35-68
16. Rendall A D 1997 Global dynamics of the mixmaster model Class. Quantum Grav. 142 341-56
17. Uggla C and von Zur-Mühlen H 1990 Compactified and reduced dynamics for locally rotationally symmetric Bianchi type IX perfect fluid models Class. Quantum Grav. 7 1365-85
18. Uggla C, Jantzen, R T, Rosquist K and von Zur-Mühlen H 1991 Remarks about late stage cosmological dynamics Gen. Rel. Grav. 23 947-66
19. Wainwright J and Ellis G F R 1997 Dynamical Systems in Cosmology (Cambridge: Cambridge University Press)
20. Wainwright J and Hsu L 1989 A dynamical systems approach to Bianchi cosmologies: orthogonal models of class A Class. Quantum Grav. 6 1409-31