Hamiltonian General Relativity and the Belinskii, Khalatnikov, Lifshitz Conjecture

Details Hamiltonian General Relativity and the Belinskii, Khalatnikov, Lifshitz Conjecture Hamiltonian General Relativity and the Belinskii, Khalatnikov, Lifshitz Conjecture

2008-11-25

arxiv.org/abs/0811.4160v2

Class.Quant.Grav.26:052001,2009

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

10 pages, 2 figures. Issue of "spikes" clarified in section IV. One reference added

Scientific paper

10.1088/0264-9381/26/5/052001

The Belinkskii, Khalatnikov and Lifshitz conjecture says that as one approaches space-like singularities in general relativity, 'time derivatives dominate over spatial derivatives' so that the dynamics at any spatial point is well captured by an ordinary differential equation. By now considerable evidence has accumulated in favor of these ideas. Starting with a Hamiltonian framework, we provide a formulation of this conjecture in terms of variables that are tailored to non-perturbative quantization. Our formulation serves as a first step in the analysis of the fate of generic space-like singularities in loop quantum gravity.

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