Hamiltonian formulation of the Belinskii-Khalatnikov-Lifshitz conjecture

Abhay Ashtekar, Adam Henderson, David Sloan

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30 Scopus citations

Abstract

The Belinskii, Khalatnikov, and Lifshitz conjecture posits that on approach to a spacelike singularity in general relativity the dynamics are well approximated by "ignoring spatial derivatives in favor of time derivatives." In A. Ashtekar, A. Henderson, and D. Sloan, Classical Quantum GravityCQGRDG0264-9381 26, 052001 (2009)10.1088/0264-9381/26/5/052001, 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.

Original languageEnglish (US)
Article number084024
JournalPhysical Review D - Particles, Fields, Gravitation and Cosmology
Volume83
Issue number8
DOIs
StatePublished - Apr 15 2011

All Science Journal Classification (ASJC) codes

  • Nuclear and High Energy Physics
  • Physics and Astronomy (miscellaneous)

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