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Well posed constraint-preserving boundary conditions for the linearized Einstein equations

Well posed constraint-preserving boundary conditions for the linearized Einstein equations
Well posed constraint-preserving boundary conditions for the linearized Einstein equations
In this paper we address the problem of specifying boundary conditions for Einstein's equations when linearized around Minkowski space using the generalized Einstein-Christoffel symmetric hyperbolic system of evolution equations. The boundary conditions we work out guarantee that the constraints are satisfied provided they are satisfied on the initial slice and ensures a well posed initial-boundary value formulation. We consider the case of a manifold with a non-smooth boundary, as is the usual case of the cubic boxes commonly used in numerical relativity. The techniques discussed should be applicable to more general cases, as linearizations around more complicated backgrounds, and may be used to establish well posedness in the full non-linear case.
0010-3616
377-395
Calabrese, Gioel
b6d18b27-64cd-426f-b86e-1b3a848f03ed
Pullin, Jorge
4c0fa15e-1ba7-49c4-bfc6-f46944951a9f
Reula, Oscar
1d224690-9074-4778-ba9e-d90bf7ef6aeb
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
Reula, Oscar
1d224690-9074-4778-ba9e-d90bf7ef6aeb
Sarbach, Olivier
9b1b946c-5ff3-4eeb-b685-915c662edff8
Tiglio, Manuel
70c1e9ee-b30c-4354-af43-1bd3b4b6af24

Calabrese, Gioel, Pullin, Jorge, Reula, Oscar, Sarbach, Olivier and Tiglio, Manuel (2003) Well posed constraint-preserving boundary conditions for the linearized Einstein equations. Communications in Mathematical Physics, 240 (1-2), 377-395. (doi:10.1007/s00220-003-0889-2).

Record type: Article

Abstract

In this paper we address the problem of specifying boundary conditions for Einstein's equations when linearized around Minkowski space using the generalized Einstein-Christoffel symmetric hyperbolic system of evolution equations. The boundary conditions we work out guarantee that the constraints are satisfied provided they are satisfied on the initial slice and ensures a well posed initial-boundary value formulation. We consider the case of a manifold with a non-smooth boundary, as is the usual case of the cubic boxes commonly used in numerical relativity. The techniques discussed should be applicable to more general cases, as linearizations around more complicated backgrounds, and may be used to establish well posedness in the full non-linear case.

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Published date: 2003

Identifiers

Local EPrints ID: 40858
URI: http://eprints.soton.ac.uk/id/eprint/40858
ISSN: 0010-3616
PURE UUID: 0e52ea2c-e70c-4001-9afd-4506cd0d7b79

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Date deposited: 11 Jul 2006
Last modified: 08 Jan 2022 18:59

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Contributors

Author: Gioel Calabrese
Author: Jorge Pullin
Author: Oscar Reula
Author: Olivier Sarbach
Author: Manuel Tiglio

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