A Hamiltonian Formulation of the BKL Conjecture

Understand

The Belinskii, Khalatnikov and Lifshitz conjecture \cite{bkl1} posits that on approach to a space-like singularity in general relativity the dynamics are well approximated by `ignoring spatial derivatives in favor of time derivatives.' In \cite{ahs1} we examined this idea from within a Hamiltonian framework and provided a new formulation of the conjecture in terms of variables well suited to loop quantum gravity.

• We now present the details of the analytical part of that investigation.
• While our motivation came from quantum considerations, thanks to some of its new features, our formulation should be useful also for future analytical and numerical investigations within general relativity.