A Hamiltonian Formulation of the BKL Conjecture

Abstract

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.

26 pages, 3 figures. Two references added. Minor typos corrected. To appear in PRD

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Cited by in corpus (45)

• Loop Quantum Cosmology: A Status Report
• Where does the physics of extreme gravitational collapse reside?
• The loop quantum cosmology bounce as a Kasner transition
• Spherical collapse in f(R) gravity and the Belinskii-Khalatnikov-Lifshitz conjecture
• Effective Dynamics in Bianchi Type II Loop Quantum Cosmology
• Through the Big Bang in inflationary cosmology
• Gravitational dynamics: A novel shift in the Hamiltonian paradigm
• A New Action for Cosmology
• When scale is surplus
• Singularity avoidance in the hybrid quantization of the Gowdy model
• Singularity-free and non-chaotic inhomogeneous Mixmaster in polymer representation for the volume of the universe
• Observations on interfacing loop quantum gravity with cosmology
• Loop Quantum Cosmology
• Bianchi IX model: Reducing phase space
• Timelike BKL singularities and chaos in AdS/CFT
• Interior dynamics of neutral and charged black holes
• Anisotropic Spinfoam Cosmology
• Loop quantum cosmology of Bianchi IX: Effective dynamics
• A critical analysis of the cosmological implementation of Loop Quantum Gravity
• Bianchi I model as a prototype for a cyclical Universe
• Semiclassical and quantum behavior of the Mixmaster model in the polymer approach for the isotropic Misner variable
• Loop quantum cosmology of Bianchi IX: Inclusion of inverse triad corrections
• A Quantum Complete Prelude to Inflation
• Hamiltonian form of `Carroll' gravity
• Past extendibility and initial singularity in Friedmann-Lemaître-Robertson-Walker and Bianchi I spacetimes
• Do spikes persist in a quantum treatment of spacetime singularities?
• Introduction to Hamiltonian Formulation of General Relativity and Homogeneous Cosmologies
• Quantum dynamics corresponding to chaotic BKL scenario
• Semiclassical and quantum features of the Bianchi I cosmology in the polymer representation
• Herglotz Action for Homogeneous Cosmology
• Mixmaster dynamics in the dust time gauge
• A Scenario for a Singularity-free Generic Cosmological Solution
• Loop Quantum Cosmology of non-diagonal Bianchi models
• Curvature from multipartite entanglement in quantum gravity states
• Reflections on the hyperbolic plane
• Hunting for gravitational quantum spikes
• Quantum Kasner transition in a locally rotationally symmetric Bianchi II universe
• Numerics of Bianchi type II and type IX spacetimes in effective loop quantum cosmology
• Anisotropic Matter in Cosmology: Locally Rotationally Symmetric Bianchi $I$ and $VI{I}_o$ Models
• Canonical Gravity in Degenerate Limit
• Deterministic evolution of gauge fields through a singularity
• Towards a general description of the interior structure of rotating black holes
• Crossing the singularity of a gravitational wave collision
• Semiclassical study of the Mixmaster model: the quantum Kasner map
• Space-like Singularities of General Relativity: A Phantom menace?