Abstract
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 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.
- Received 21 October 2002
DOI:https://doi.org/10.1103/PhysRevD.68.064013
©2003 American Physical Society