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Symmetric hyperbolicity and consistent boundary conditions for second-order Einstein equations

Symmetric hyperbolicity and consistent boundary conditions for second-order Einstein equations
Symmetric hyperbolicity and consistent boundary conditions for second-order Einstein equations
We present two families of first-order in time and second-order in space formulations of the Einstein equations (variants of the Arnowitt-Deser-Misner formulation) that admit a complete set of characteristic variables and a conserved energy that can be expressed in terms of the characteristic variables. The associated constraint system is also symmetric hyperbolic in this sense, and all characteristic speeds are physical. We propose a family of constraint-preserving boundary conditions that is applicable if the boundary is smooth with tangential shift. We conjecture that the resulting initial-boundary value problem is well-posed.
1550-7998
044032-[16pp]
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. (2004) Symmetric hyperbolicity and consistent boundary conditions for second-order Einstein equations. Physical Review D, 70 (4), 044032-[16pp]. (doi:10.1103/PhysRevD.70.044032).

Record type: Article

Abstract

We present two families of first-order in time and second-order in space formulations of the Einstein equations (variants of the Arnowitt-Deser-Misner formulation) that admit a complete set of characteristic variables and a conserved energy that can be expressed in terms of the characteristic variables. The associated constraint system is also symmetric hyperbolic in this sense, and all characteristic speeds are physical. We propose a family of constraint-preserving boundary conditions that is applicable if the boundary is smooth with tangential shift. We conjecture that the resulting initial-boundary value problem is well-posed.

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Published date: 2004

Identifiers

Local EPrints ID: 29198
URI: https://eprints.soton.ac.uk/id/eprint/29198
ISSN: 1550-7998
PURE UUID: c879a8de-b025-419c-8f58-5ee1c4b55781
ORCID for Carsten Gundlach: ORCID iD orcid.org/0000-0001-9585-5375

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Date deposited: 12 May 2006
Last modified: 20 Jul 2018 00:34

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