Adiabatic invariants and Mixmaster catastrophes

Details Adiabatic invariants and Mixmaster catastrophes Adiabatic invariants and Mixmaster catastrophes

1997-12-04

arxiv.org/abs/gr-qc/9712027v1

Phys.Rev. D57 (1998) 4691-4698

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

24 pages, LaTeX, 5 figures (which can be obtained by sending a message to the first author), submitted to Phys.Rev.D

Scientific paper

10.1103/PhysRevD.57.4691

We present a rigorous analysis of the role and uses of the adiabatic invariant in the Mixmaster dynamical system. We propose a new invariant for the global dynamics which in some respects has an improved behaviour over the commonly used one. We illustrate its behaviour in a number of numerical results. We also present a new formulation of the dynamics via Catastrophe Theory. We find that the change from one era to the next corresponds to a fold catastrophe, during the Kasner shifts the potential is an Implicit Function Form whereas, as the anisotropy dissipates, the Mixmaster potential must become a Morse 0--saddle. We compare and contrast our results to many known works on the Mixmaster problem and indicate how extensions could be achieved. Further exploitation of this formulation may lead to a clearer understanding of the global Mixmaster dynamics.

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