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Well-posedness of formulations of the Einstein equations with dynamical lapse and shift conditions

Well-posedness of formulations of the Einstein equations with dynamical lapse and shift conditions
Well-posedness of formulations of the Einstein equations with dynamical lapse and shift conditions
We prove that when the equations are restricted to the principal part the standard version of the Baumgarte-Shapiro-Shibata-Nakamura (BSSN) formulation of the Einstein equations is equivalent to the Nagy-Ortiz-Reula (NOR) formulation for any gauge, and that the Kidder-Scheel-Teukolsky (KST) formulation is equivalent to NOR for a variety of gauges. We review a family of elliptic gauge conditions and the implicit parabolic and hyperbolic drivers that can be derived from them, and show how to make them symmetry-seeking. We investigate the hyperbolicity of Arnowitt-Deser-Misner (ADM), NOR, and BSSN with implicit hyperbolic lapse and shift drivers. We show that BSSN with the coordinate drivers used in recent "moving puncture" binary black hole evolutions is ill-posed at large shifts, and suggest how to make it strongly hyperbolic for arbitrary shifts. For ADM, NOR, and BSSN with elliptic and parabolic gauge conditions, which cannot be hyperbolic, we investigate a necessary condition for well-posedness of the initial-value problem.
1550-7998
024016-[19]
Gundlach, Carsten
586f1eb5-3185-4b2b-8656-c29c436040fc
Martín-García, José M.
4d46af63-2651-477e-b0f0-67245eba67f0
Gundlach, Carsten
586f1eb5-3185-4b2b-8656-c29c436040fc
Martín-García, José M.
4d46af63-2651-477e-b0f0-67245eba67f0

Gundlach, Carsten and Martín-García, José M. (2006) Well-posedness of formulations of the Einstein equations with dynamical lapse and shift conditions. Physical Review D, 74 (2), 024016-[19]. (doi:10.1103/PhysRevD.74.024016).

Record type: Article

Abstract

We prove that when the equations are restricted to the principal part the standard version of the Baumgarte-Shapiro-Shibata-Nakamura (BSSN) formulation of the Einstein equations is equivalent to the Nagy-Ortiz-Reula (NOR) formulation for any gauge, and that the Kidder-Scheel-Teukolsky (KST) formulation is equivalent to NOR for a variety of gauges. We review a family of elliptic gauge conditions and the implicit parabolic and hyperbolic drivers that can be derived from them, and show how to make them symmetry-seeking. We investigate the hyperbolicity of Arnowitt-Deser-Misner (ADM), NOR, and BSSN with implicit hyperbolic lapse and shift drivers. We show that BSSN with the coordinate drivers used in recent "moving puncture" binary black hole evolutions is ill-posed at large shifts, and suggest how to make it strongly hyperbolic for arbitrary shifts. For ADM, NOR, and BSSN with elliptic and parabolic gauge conditions, which cannot be hyperbolic, we investigate a necessary condition for well-posedness of the initial-value problem.

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More information

Submitted date: 8 April 2006
Published date: July 2006

Identifiers

Local EPrints ID: 48963
URI: https://eprints.soton.ac.uk/id/eprint/48963
ISSN: 1550-7998
PURE UUID: 889ce434-147d-4009-9c35-0cac9a7e0ba3
ORCID for Carsten Gundlach: ORCID iD orcid.org/0000-0001-9585-5375

Catalogue record

Date deposited: 18 Oct 2007
Last modified: 20 Jul 2018 00:34

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