Dynamics of magnetic Bianchi VI_0 cosmologies

Details Dynamics of magnetic Bianchi VI_0 cosmologies Dynamics of magnetic Bianchi VI_0 cosmologies

1999-09-14

arxiv.org/abs/gr-qc/9909043v4

Class.Quant.Grav. 17 (2000) 421-434

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

14 pages, 1 figure. Final version

Scientific paper

10.1088/0264-9381/17/2/311

Methods of dynamical systems analysis are used to show rigorously that the presence of a magnetic field orthogonal to the two commuting Killing vector fields in any spatially homogeneous Bianchi type VI_0 vacuum solution to Einstein's equation changes the evolution toward the singularity from convergent to oscillatory. In particular, it is shown that the alpha-limit set (for time direction that puts the singularity in the past) of any of these magnetic solutions contains at least two sequential Kasner points of the BKL sequence and the orbit of the transition solution between them. One of the Kasner points in the alpha-limit set is non-flat, which leads to the result that each of these magnetic solutions has a curvature singularity.

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