Filtered expansions in general relativity I
arXiv:1905.09026
Abstract
This is the first of two papers in which we construct formal power series solutions in external parameters to the vacuum Einstein equations, implementing one bounce for the Belinskii-Khalatnikov-Lifshitz (BKL) proposal for spatially inhomogeneous spacetimes. We use a graded Lie algebra, homological framework. A dedicated filtration encodes key features of the BKL proposal, and we use it to set up an unobstructed perturbative problem.
22 pages