The cosmological billiard attractor
Abstract
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.
- Publication:
-
arXiv e-prints
- Pub Date:
- February 2007
- DOI:
- arXiv:
- arXiv:gr-qc/0702141
- Bibcode:
- 2007gr.qc.....2141H
- Keywords:
-
- General Relativity and Quantum Cosmology
- E-Print:
- 88 pages, 18 figures