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://ucris.univie.ac.at/portal/en/publications/the-cosmological-billiard-attractor(8388f170-449e-47aa-a07a-59fe903e7638).html