2004
DOI: 10.1017/s0305004104007960
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Asymptotic behaviour of the Einstein–Vlasov system with a positive cosmological constant

Abstract: Abstract. We study locally spatially homogeneous solutions of the EinsteinVlasov system with a positive cosmological constant. First the global existence of solutions of this system and the casual geodesic completeness are shown. Then the asymptotic behaviour of solutions in the future time is investigated in various aspects.

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Cited by 103 publications
(126 citation statements)
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“…By construction the evolution equation (12) is satisfied for all values of m except possibly m = n and m = 2n while (11) is satisfied except possibly for m = n. The fact B ab has zero trace ensures that (12) is satisfied while (11) is automatic for m = n. These statements make use of the fact that the odd order coefficients of k a b of order less than n vanish. It will now be shown by induction that (11)- (14) hold for all m. Except for m = 2n only (13) and (14) need to be verified. The equations (11)- (14) hold for m = 1.…”
Section: Perturbative Solutionsmentioning
confidence: 99%
“…By construction the evolution equation (12) is satisfied for all values of m except possibly m = n and m = 2n while (11) is satisfied except possibly for m = n. The fact B ab has zero trace ensures that (12) is satisfied while (11) is automatic for m = n. These statements make use of the fact that the odd order coefficients of k a b of order less than n vanish. It will now be shown by induction that (11)- (14) hold for all m. Except for m = 2n only (13) and (14) need to be verified. The equations (11)- (14) hold for m = 1.…”
Section: Perturbative Solutionsmentioning
confidence: 99%
“…This is analogous to the refinement of Wald's theorem proved by Lee [6]. The first step is to determine the leading order asymptotics of tr k. From the modified Hamiltonian constraint and the estimates already obtained it follows that…”
Section: Isotropization Near Big Rip Singularitiesmentioning
confidence: 73%
“…The particle has energy −k/2 as a consequence of (6). The picture with the potential is useful for giving an intuitive method for seeing how the dynamics looks.…”
Section: Isotropic Modelsmentioning
confidence: 99%
“…This conjecture states roughly speaking that all expanding cosmological models with a positive cosmological constant approach asymptotically the de Sitter solution. For the EinsteinVlasov system isotropization could be shown for all non-type IX Bianchi cosmologies [19].…”
Section: Introductionmentioning
confidence: 94%