Hunting Local Mixmaster Dynamics in Spatially Inhomogeneous Cosmologies

Abstract

Heuristic arguments and numerical simulations support the Belinskii et al (BKL) claim that the approach to the singularity in generic gravitational collapse is characterized by local Mixmaster dynamics (LMD). Here, one way to identify LMD in collapsing spatially inhomogeneous cosmologies is explored. By writing the metric of one spacetime in the standard variables of another, signatures for LMD may be found. Such signatures for the dynamics of spatially homogeneous Mixmaster models in the variables of U(1)-symmetric cosmologies are reviewed. Similar constructions for U(1)-symmetric spacetimes in terms of the dynamics of generic $T^2$-symmetric spacetime are presented.

17 pages, 5 figures. Contribution to CQG Special Issue "A Spacetime Safari: Essays in Honour of Vincent Moncrief"

References in corpus (3)

• Numerical Approaches to Spacetime Singularities
• The past attractor in inhomogeneous cosmology
• Quantum Dynamics of the Polarized Gowdy Model

Cited by in corpus (4)

• Classical and Quantum Features of the Mixmaster Singularity
• Cosmological models from a dynamical systems perspective
• Bianchi I "asymptotically Kasner" solutions of the Einstein scalar field equations
• Anisotropic Matter in Cosmology: Locally Rotationally Symmetric Bianchi $I$ and $VI{I}_o$ Models