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Well Posed Constraint-Preserving Boundary Conditions for the Linearized Einstein Equations

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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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Authors and Affiliations

  1. Department of Physics and Astronomy, Louisiana State University, 202 Nicholson Hall, Baton Rouge, LA 70803-4001, USA

    Gioel Calabrese, Jorge Pullin, Olivier Sarbach & Manuel Tiglio

  2. Facultad de Matemática, Astronomía y Física, Universidad Nacional de Córdoba, Ciudad Universitaria, 5000, Córdoba, Argentina

    Oscar Reula

Authors
  1. Gioel Calabrese
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  2. Jorge Pullin
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  3. Oscar Reula
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  4. Olivier Sarbach
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  5. Manuel Tiglio
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Communicated by H. Nicolai

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Calabrese, G., Pullin, J., Reula, O. et al. Well Posed Constraint-Preserving Boundary Conditions for the Linearized Einstein Equations. Commun. Math. Phys. 240, 377–395 (2003). https://doi.org/10.1007/s00220-003-0889-2

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  • DOI: https://doi.org/10.1007/s00220-003-0889-2

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