How to determine approximate Mixmaster parameters from numerical evolution of Einstein's equations

TL;DR

This paper presents an algorithm to extract approximate Mixmaster parameters from numerical solutions of Einstein's equations, aiding the validation of the BKL approximation in Mixmaster dynamics.

Contribution

The authors develop a novel algorithm to determine BKL parameters directly from numerical Einstein solutions, providing a practical tool for analyzing Mixmaster behavior.

Findings

Algorithm successfully extracts BKL parameters from numerical data.

Results demonstrate the method's effectiveness on typical trajectories.

Supports the use of BKL approximation in complex gravitational simulations.

Abstract

To assess the validity of the Belinskii, Khalatnikov, and Lifshitz (BKL) approximation to Mixmaster dynamics, it would be useful to evaluate the BKL discrete parameters as a byproduct of the numerical solution of Einstein's equations. An algorithm to do this and results for a typical trajectory are presented.