 
Summary: New firstorder formulation for the Einstein equations
Alexander M. Alekseenko*
School of Mathematics, University of Minnesota, Minneapolis, Minnesota 55455, USA
Douglas N. Arnold
Institute for Mathematics and Its Applications, University of Minnesota, Minneapolis, Minnesota 55455, USA
Received 21 October 2002; published 23 September 2003
We derive a new firstorder formulation for Einstein's equations which involves fewer unknowns than other
firstorder formulations that have been proposed. The new formulation is based on the 3 1 decomposition
with arbitrary lapse and shift. In the reduction to firstorder 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.
DOI: 10.1103/PhysRevD.68.064013 PACS number s : 04.20.Ex, 04.25.Dm
I. INTRODUCTION
Many ways have been proposed to formulate Einstein's
equations of general relativity in a manner suitable for nu
meric computation. In this paper we introduce a new first
order formulation for Einstein's equations. This system in
volves fewer unknowns than other firstorder formulations
