Astronomy and Astrophysics – Astrophysics – General Relativity and Quantum Cosmology
Scientific paper
2007-02-27
Adv.Theor.Math.Phys.13:293-407,2009
Astronomy and Astrophysics
Astrophysics
General Relativity and Quantum Cosmology
88 pages, 18 figures
Scientific paper
This article is devoted to a study of the asymptotic dynamics of generic solutions of the Einstein vacuum equations toward a generic spacelike singularity. Starting from fundamental assumptions about the nature of generic spacelike singularities we derive in a step-by-step manner the cosmological billiard conjecture: we show that the generic asymptotic dynamics of solutions is represented by (randomized) sequences of heteroclinic orbits on the `billiard attractor'. Our analysis rests on two pillars: (i) a dynamical systems formulation based on the conformal Hubble-normalized orthonormal frame approach expressed in an Iwasawa frame; (ii) stochastic methods and the interplay between genericity and stochasticity. Our work generalizes and improves the level of rigor of previous work by Belinskii, Khalatnikov, and Lifshitz; furthermore, we establish that our approach and the Hamiltonian approach to `cosmological billiards', as elaborated by Damour, Hennaux, and Nicolai, can be viewed as yielding `dual' representations of the asymptotic dynamics.
Heinzle Mark J.
Rohr Niklas
Uggla Claes
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