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Lifshitz E.M. and Khalatnikov I.M., Adv. Phys. 12 (1963), 185-249
1963
Earlier work this paper cites.
Gerstenhaber M., Ann. of Math. 79 (1964), 59-103
1964
Earlier work this paper cites.

Similar

Nijenhuis A. and Richardson R.W. Jr., Bull. Amer. Math. Soc. 70 (1964), 406-411
1964
Cited alongside, same era.
Belinskii V.A., Khalatnikov I.M. and Lifshitz E.M., Adv. Phys. 19 (1970), 525-573
1982
Cited alongside, same era.
Reiterer M. and Trubowitz E., arxiv.org/abs/1412.5561
Original
Cited in the paper.

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Chow T.Y., Notices of the AMS, January 2006
2006
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2015

Filtered expansions in general relativity and one BKL-bounce

Reiterer, Michael, Trubowitz, Eugene

Understand

When the vacuum Einstein equations are formulated in terms of a frame, rather than a metric, can one perturb solutions with a degenerate frame into ones with a nondegenerate frame? In examples we point out that one can encounter issues already at the level of formal perturbative expansions; namely the cohomological, so-called space of obstructions is nonzero.

In this paper we propose a perturbative expansion based on filtrations.
We construct and prove properties of a specific filtration, intended to make mathematical sense of one BKL-bounce, a building block of a well-known but very heuristic conjecture due to Belinskii, Khalatnikov and Lifshitz (which would involve sticking together an infinite sequence of single bounces).
It seems possible that now the space of obstructions is zero, but this question is left open.