New Algorithm for Mixmaster Dynamics

Details New Algorithm for Mixmaster Dynamics New Algorithm for Mixmaster Dynamics

1996-09-30

arxiv.org/abs/gr-qc/9609072v1

Class.Quant.Grav.14:L29-L36,1997

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

12 pages, Revtex, 4 eps figures

Scientific paper

10.1088/0264-9381/14/2/001

We present a new numerical algorithm for evolving the Mixmaster spacetimes. By using symplectic integration techniques to take advantage of the exact Taub solution for the scattering between asymptotic Kasner regimes, we evolve these spacetimes with higher accuracy using much larger time steps than previously possible. The longer Mixmaster evolution thus allowed enables detailed comparison with the Belinskii, Khalatnikov, Lifshitz (BKL) approximate Mixmaster dynamics. In particular, we show that errors between the BKL prediction and the measured parameters early in the simulation can be eliminated by relaxing the BKL assumptions to yield an improved map. The improved map has different predictions for vacuum Bianchi Type IX and magnetic Bianchi Type VI$_0$ Mixmaster models which are clearly matched in the simulation.

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