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arXiv · gr-qc/0701093

Covariant Description of the Inhomogeneous Mixmaster Chaos

Riccardo Benini·Giovanni Montani
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Abstract

We outline the covariant nature of the chaos characterizing the generic cosmological solution near the initial singularity. Our analysis is based on a "gauge" independent ADM-reduction of the dynamics to the physical degrees of freedom, and shows that the dynamics is isomorphic point by point in space to a billiard on a Lobachevsky plane. The Jacobi metric associated to the geodesic flow is constructed and a non-zero Lyapunov exponent is explicitly calculated. The chaos covariance emerges from the independence of the form of the lapse function and the shift vector.

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Riccardo Benini, Giovanni Montani. 2007-01-16. Covariant Description of the Inhomogeneous Mixmaster Chaos. https://doi.org/10.1142/9789812834300_0272

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