New first-order formulation for the Einstein equations

Details New first-order formulation for the Einstein equations New first-order formulation for the Einstein equations

2002-10-21

arxiv.org/abs/gr-qc/0210071v2

Phys.Rev. D68 (2003) 064013

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

6 pages

Scientific paper

10.1103/PhysRevD.68.064013

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.

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