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.
044032-[16pp]
Gundlach, Carsten
586f1eb5-3185-4b2b-8656-c29c436040fc
Martín-García, José M.
4d46af63-2651-477e-b0f0-67245eba67f0
2004
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), .
(doi:10.1103/PhysRevD.70.044032).
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
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Local EPrints ID: 29198
URI: http://eprints.soton.ac.uk/id/eprint/29198
ISSN: 1550-7998
PURE UUID: c879a8de-b025-419c-8f58-5ee1c4b55781
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Date deposited: 12 May 2006
Last modified: 16 Mar 2024 03:15
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Author:
José M. Martín-García
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