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2014

The graded Lie algebra of general relativity

Reiterer, Michael, Trubowitz, Eugene

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We construct a graded Lie algebra in which a solution to the vacuum Einstein equations is any element of degree 1 whose bracket with itself is zero.

Each solution generates a cochain complex, whose first cohomology is linearized gravity about that solution.
We gauge-fix to get a smaller cochain complex with the same cohomologies (deformation retraction).
The new complex is much smaller, it consists of the solution spaces of linear homogeneous wave equations (symmetric hyperbolic equations).

The graded Lie algebra of general relativity · Around

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Friedrichs K.O., Comm. Pure and Appl. Math. 7, 2, (1954) 345-392
1954
Earlier work this paper cites.
Newman E. and Penrose R.J., J. Math. Phys. 3, (1962) 566-578
1962
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.
Friedrich H., Proc. R. Soc. Lond. A 375, (1981) 169-184
1981
Cited alongside, same era.
Reiterer M. and Trubowitz E., arxiv.org/abs/0910.4666v1
Original
Cited in the paper.
Reiterer M. and Trubowitz E., arxiv.org/abs/1104.4972v2
Original
Cited in the paper.
Taylor M.E.,
Cited in the paper.

Then

Reiterer M. and Trubowitz E., Comm. Math. Phys., 307, 2, (2011) 275-313
2011
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