Hunting Local Mixmaster Dynamics in Spatially Inhomogeneous Cosmologies

TL;DR

This paper investigates how local Mixmaster dynamics manifest in spatially inhomogeneous cosmologies approaching singularity, using metric transformations and signatures to identify characteristic behaviors.

Contribution

It introduces a method to detect local Mixmaster dynamics in inhomogeneous cosmologies by analyzing metric signatures in different variable frameworks.

Findings

Signatures for LMD identified in U(1)-symmetric models

Construction of signatures in T^2-symmetric spacetimes

Review of dynamics in homogeneous Mixmaster models

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.