Test Case for Identification of Local Mixmaster Dynamics in Generic Gravitational Collapse

Details Test Case for Identification of Local Mixmaster Dynamics in Generic Gravitational Collapse Test Case for Identification of Local Mixmaster Dynamics in Generic Gravitational Collapse

May 2004

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2004aps..aprs13001b&link_type=abstract

American Physical Society, April Meeting, 2004, May 1-4, 2004, Denver, Colorado April 2004, MEETING ID: APR04, abstract #S13.001

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Belinskii, Khalatnikov, and Lifshitz (BKL) conjectured long ago that, sufficiently close to the singularity, generic collapse could be characterized as effectively independent evolutions at each spatial point with the local evolution that of a spatially homogeneous cosmology. BKL expected the most general case to exhibit the Mixmaster dynamics of Bianchi IX models. Such behavior may be described by the BKL parameter u, constant in any Mixmaster epoch but decreasing by 1 from epoch to epoch until the end of an era (1 ≤ u < 2) when u → (u -1)-1. In spatially homogeneous cosmologies, the value of u may be extracted during a computer simulation by expressing it as a function of ratios of extrinsic curvature components. More generally, it is possible to identify (spatial) invariants involving the extrinsic curvature that contain the same information as u to allow identification of local Mixmaster dynamics in simulations of generic gravitational collapse. As a test case, the algorithm for extraction of u in the general case was applied to the numerical evolution of collapsing, generic T^2-symmetric spacetimes. The comparison between this approach and other ways to identify local Mixmaster dynamics will be made.

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