Hidden symmetries in mixmaster-type universe
Abstract
A model of multidimensional mixmaster-type vacuum universe is considered. It belongs to a class of pseudo-Euclidean chains characterized by root vectors. An algebraic approach of our investigation is founded on construction of Cartan matrix of the spacelike root vectors in Wheeler -- DeWitt space. Kac -- Moody algebras can be classified according to their Cartan matrix. By this way a hidden symmetry of the model considered is revealed. It is known, that gravitational models which demonstrate chaotic behavior are associated with hyperbolic Kac -- Moody algebras. The algebra considered in our paper is not hyperbolic. The square of Weyl vector is negative. The mixmaster-type universe is associated with a simply-laced Lorentzian Kac -- Moody algebra. Since the volume of the configuration space is infinite, the model is not chaotic.
Keywords
Cite
@article{arxiv.1805.12329,
title = {Hidden symmetries in mixmaster-type universe},
author = {Alexander Pavlov},
journal= {arXiv preprint arXiv:1805.12329},
year = {2019}
}
Comments
10 pages, 2 figures, submitted to General Relativity and Gravitation 4 July 2017