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Stability properties of a formulation of Einstein's equations

Stability properties of a formulation of Einstein's equations
Stability properties of a formulation of Einstein's equations
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 space-time, 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 learned in this analysis can be applied in other formulations with similar properties.
1550-7998
1-12
Calabrese, Gioel
b6d18b27-64cd-426f-b86e-1b3a848f03ed
Pullin, Jorge
4c0fa15e-1ba7-49c4-bfc6-f46944951a9f
Sarbach, Olivier
9b1b946c-5ff3-4eeb-b685-915c662edff8
Tiglio, Manuel
70c1e9ee-b30c-4354-af43-1bd3b4b6af24
Calabrese, Gioel
b6d18b27-64cd-426f-b86e-1b3a848f03ed
Pullin, Jorge
4c0fa15e-1ba7-49c4-bfc6-f46944951a9f
Sarbach, Olivier
9b1b946c-5ff3-4eeb-b685-915c662edff8
Tiglio, Manuel
70c1e9ee-b30c-4354-af43-1bd3b4b6af24

Calabrese, Gioel, Pullin, Jorge, Sarbach, Olivier and Tiglio, Manuel (2002) Stability properties of a formulation of Einstein's equations. Physical Review D, 66 (6), 1-12. (doi:10.1103/PhysRevD.66.064011).

Record type: Article

Abstract

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 space-time, 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 learned in this analysis can be applied in other formulations with similar properties.

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Published date: 2002

Identifiers

Local EPrints ID: 40860
URI: http://eprints.soton.ac.uk/id/eprint/40860
ISSN: 1550-7998
PURE UUID: 23751b04-cd63-4cea-8198-7003f931af8b

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Date deposited: 11 Jul 2006
Last modified: 15 Jul 2019 18:58

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