The Lifshitz-Khalatnikov Kasner index parametrization and the Weyl Tensor
Abstract
The scale invariant Petrov classification of the Weyl tensor is linked to the scale invariant combination of the Kasner index constraints, and the Lifshitz-Khalatnikov Kasner index parametrization scheme turns out to be a natural way of adapting to this symmetry, while hiding the permutation symmetry that is instead made manifest by the Misner parametrization scheme. While not so interesting for the Kasner spacetime by itself, it gives a geometrical meaning to the famous Kasner map transitioning between Kasner epochs and Kasner eras, equivalently bouncing between curvature walls, in the BLK-Mixmaster dynamics exhibited by spatially homogeneous cosmologies approaching the initial cosmological singularity and the inhomogeneous generalization of this dynamics.
Cite
@article{arxiv.0710.4902,
title = {The Lifshitz-Khalatnikov Kasner index parametrization and the Weyl Tensor},
author = {Donato Bini and Christian Cherubini and Robert T. Jantzen},
journal= {arXiv preprint arXiv:0710.4902},
year = {2010}
}
Comments
16 page Latex cimento.cls formatted document with 6 EPS figures annd 2 PicTeX figures; to appear in the Proceedings of the First Italian-Pakistan Workshop on Relativistic Astrophysics which will be published as a special issue of Nuovo Cimento B