New first-order formulation for the Einstein equations

Alexander M. Alekseenko, Douglas N. Arnold

Research output: Contribution to journalArticlepeer-review

7 Scopus citations


We derive a new first-order formulation for Einstein's equations which involves fewer unknowns than other first-order formulations that have been proposed. The new formulation is based on the 3 + 1 decomposition with arbitrary lapse and shift. In the reduction to first-order form only eight particular combinations of the 18 first derivatives of the spatial metric are introduced. In the case of linearization about Minkowski space, the new formulation consists of a symmetric hyperbolic system in 14 unknowns, namely, the components of the extrinsic curvature perturbation and the eight new variables, from whose solution the metric perturbation can be computed by integration.

Original languageEnglish (US)
Article number064013
JournalPhysical Review D
Issue number6
StatePublished - 2003


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