Stability properties of a formulation of Einstein's equations

Details Stability properties of a formulation of Einstein's equations Stability properties of a formulation of Einstein's equations

2002-05-16

arxiv.org/abs/gr-qc/0205073v1

Phys.Rev. D66 (2002) 064011

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

17 Pages, RevTex, 16 figures

Scientific paper

10.1103/PhysRevD.66.064011

We study the stability properties of the Kidder-Scheel-Teukolsky (KST) many-parameter formulation of Einstein's equations for weak gravitational waves on flat space-time from a continuum and numerical point of view. At the continuum, performing a linearized analysis of the equations around flat spacetime, it turns out that they have, essentially, no non-principal terms. As a consequence, in the weak field limit the stability properties of this formulation depend only on the level of hyperbolicity of the system. At the discrete level we present some simple one-dimensional simulations using the KST family. The goal is to analyze the type of instabilities that appear as one changes parameter values in the formulation. Lessons learnt in this analysis can be applied in other formulations with similar properties.

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