Hamiltonian General Relativity and the Belinskii, Khalatnikov, Lifshitz Conjecture

Abstract

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.

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

References in corpus (9)

• Quiescent cosmological singularities
• Numerical Approaches to Spacetime Singularities
• The past attractor in inhomogeneous cosmology
• Numerical simulations of generic singuarities
• The behavior of non-linear anisotropies in bouncing Bianchi I models of loop quantum cosmology
• Numerical simulations of general gravitational singularities
• Geometrodynamics vs. Connection Dynamics
• New explicit spike solution -- non-local component of the generalized Mixmaster attractor
• Geometrical representation of Euclidean general relativity in the canonical formalism

Cited by in corpus (27)

• Loop Quantum Cosmology: A Status Report
• Loop quantum cosmology of Bianchi I models
• Loop quantum cosmology of Bianchi type IX models
• A Hamiltonian Formulation of the BKL Conjecture
• The loop quantum cosmology bounce as a Kasner transition
• Gravitational dynamics: A novel shift in the Hamiltonian paradigm
• Symmetry Reduction of Loop Quantum Gravity
• Probing the Big Bang with quantum fields
• Lorentz Symmetry in QFT on Quantum Bianchi I Space-Time
• Loop Quantum Cosmology
• Timelike BKL singularities and chaos in AdS/CFT
• The Big Bang and the Quantum
• Anisotropic Spinfoam Cosmology
• Symmetry Reduced Loop Quantum Gravity: A Bird's Eye View
• Semiclassical and quantum behavior of the Mixmaster model in the polymer approach for the isotropic Misner variable
• A Quantum Complete Prelude to Inflation
• Hamiltonian form of `Carroll' gravity
• Introduction to Hamiltonian Formulation of General Relativity and Homogeneous Cosmologies
• Quantum dynamics corresponding to chaotic BKL scenario
• Phenomenology of a massive quantum field in a cosmological quantum spacetime
• Reflections on the hyperbolic plane
• Anisotropic Matter in Cosmology: Locally Rotationally Symmetric Bianchi $I$ and $VI{I}_o$ Models
• Numerics of Bianchi type II and type IX spacetimes in effective loop quantum cosmology
• Canonical Gravity in Degenerate Limit
• Crossing the singularity of a gravitational wave collision
• Space-like Singularities of General Relativity: A Phantom menace?
• Examination of the nature of the Bianchi type cosmological singularities