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 8 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 symmetric hyperbolic system in 14 unknowns, namely the components of the extrinsic curvature perturbation and the 8 new variables, from whose solution the metric perturbation can be computed by integration.
Institute for Mathematics and Its Applications>IMA Preprints Series
Alekseenko, Alexander M.; Arnold, Douglas N..
New first-order formulation for the Einstein equations.
Retrieved from the University of Minnesota Digital Conservancy,
Content distributed via the University of Minnesota's Digital Conservancy may be subject to additional license and use restrictions applied by the depositor.