The cosmological billiard attractor
- Author(s)
- Johannes Markus Heinzle, Niklas Röhr, Claes Uggla
- 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.
- Organisation(s)
- Gravitational Physics
- External organisation(s)
- Karlstad University
- Journal
- Advances in Theoretical and Mathematical Physics
- Volume
- 13
- Pages
- 293-407
- No. of pages
- 114
- ISSN
- 1095-0761
- DOI
- https://doi.org/10.4310/ATMP.2009.v13.n2.a1
- Publication date
- 2009
- Peer reviewed
- Yes
- Austrian Fields of Science 2012
- 103028 Theory of relativity
- Portal url
- https://ucrisportal.univie.ac.at/en/publications/8388f170-449e-47aa-a07a-59fe903e7638