The cosmological billiard attractor

Autor(en)

Johannes Markus Heinzle, Niklas Röhr, Claes Uggla

Abstrakt

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(en)

Gravitationsphysik

Externe Organisation(en)

Karlstad University

Journal

Advances in Theoretical and Mathematical Physics

Band

13

Seiten

293-407

Anzahl der Seiten

114

ISSN

1095-0761

DOI

https://doi.org/10.4310/ATMP.2009.v13.n2.a1

Publikationsdatum

2009

Peer-reviewed

Ja

ÖFOS 2012

103028 Relativitätstheorie

Link zum Portal

https://ucrisportal.univie.ac.at/de/publications/8388f170-449e-47aa-a07a-59fe903e7638