Generic instability of the dynamics underlying the Belinski-Khalatnikov-Lifshitz scenario
General Relativity and Quantum Cosmology
2022-03-30 v3 Mathematical Physics
math.MP
Exactly Solvable and Integrable Systems
Abstract
A class of exact solutions to the Belinski-Khalatnikov-Lifshitz (BKL) scenario is derived and tested for their stability against small perturbations. These are the only regular solutions in the Painlev\'{e} sense. We prove that they are unstable in the vicinity of the cosmological singularity. Regularity of the dynamics is also examined with the dynamical systems method. Our results confirm the conjecture of BKL that the dynamics near the singularity becomes generically chaotic.
Keywords
Cite
@article{arxiv.2103.16145,
title = {Generic instability of the dynamics underlying the Belinski-Khalatnikov-Lifshitz scenario},
author = {Piotr Goldstein and Włodzimierz Piechocki},
journal= {arXiv preprint arXiv:2103.16145},
year = {2022}
}
Comments
17 pages, 3 figures, version accepted for publication in EPJC