Long wavelength iteration of Einstein's equations near a spacetime singularity

Details Long wavelength iteration of Einstein's equations near a spacetime singularity Long wavelength iteration of Einstein's equations near a spacetime singularity

1994-11-15

arxiv.org/abs/gr-qc/9411040v1

Phys.Rev. D52 (1995) 2007-2019

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

35 pages, revtex, no figures

Scientific paper

10.1103/PhysRevD.52.2007

We clarify the links between a recently developped long wavelength iteration scheme of Einstein's equations, the Belinski Khalatnikov Lifchitz (BKL) general solution near a singularity and the antinewtonian scheme of Tomita's. We determine the regimes when the long wavelength or antinewtonian scheme is directly applicable and show how it can otherwise be implemented to yield the BKL oscillatory approach to a spacetime singularity. When directly applicable we obtain the generic solution of the scheme at first iteration (third order in the gradients) for matter a perfect fluid. Specializing to spherical symmetry for simplicity and to clarify gauge issues, we then show how the metric behaves near a singularity when gradient effects are taken into account.

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