The Lifshitz-Khalatnikov Kasner index parametrization and the Weyl Tensor

Details The Lifshitz-Khalatnikov Kasner index parametrization and the Weyl Tensor The Lifshitz-Khalatnikov Kasner index parametrization and the Weyl Tensor

2007-10-25

arxiv.org/abs/0710.4902v1

Nuovo Cim.B122:521-536,2007

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

16 page Latex cimento.cls formatted document with 6 EPS figures annd 2 PicTeX figures; to appear in the Proceedings of the Fir

Scientific paper

10.1393/ncb/i2007-10396-4

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.

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