2007
DOI: 10.1088/0264-9381/24/24/012
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Outer boundary conditions for Einstein's field equations in harmonic coordinates

Abstract: We analyze Einstein's vacuum field equations in generalized harmonic coordinates on a compact spatial domain with boundaries. We specify a class of boundary conditions, which is constraint-preserving and sufficiently general to include recent proposals for reducing the amount of spurious reflections of gravitational radiation. In particular, our class comprises the boundary conditions recently proposed by Kreiss and Winicour, a geometric modification thereof, the freezing-0 boundary condition and the hierarchy… Show more

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Cited by 40 publications
(117 citation statements)
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References 43 publications
(236 reference statements)
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“…Since the determinant condition is satisfied we can solve (A8) for the integration constants. What remains to be shown is that solution (A7) can be bounded in terms of the data given at the boundary, According to [19,23], one can show that there is a constant δ > 0 such that…”
Section: Discussionmentioning
confidence: 99%
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“…Since the determinant condition is satisfied we can solve (A8) for the integration constants. What remains to be shown is that solution (A7) can be bounded in terms of the data given at the boundary, According to [19,23], one can show that there is a constant δ > 0 such that…”
Section: Discussionmentioning
confidence: 99%
“…Nevertheless, the integration constant σ satisfies a m+1 + σ =g. It can be shown that the system (B6) with BCs (B19) is boundary stable and, according to [23], the solution satisfies the following estimate …”
Section: Discussionmentioning
confidence: 99%
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“…The evolution equation (12) has the form (1) where E is the vector bundle of symmetric, covariant tensor fields on M and the boundary conditions (14)(15)(16)(17)(18)(19)(20) have the form (3) where α = 1 and c a bc…”
Section: B Maxwell's Equations In the Lorentz Gaugementioning
confidence: 99%
“…This equation (minus the constraint-damping terms) was derived previously by Ruiz, Rinne and Sarbach [11], who used it in their analysis of boundary conditions, and by Brown [12], who used it to derive an action principle for this second-order covariant generalized harmonic formulation of Einstein's equation. The idea now is to transform Eq.…”
Section: Covariant First-order Einstein Evolution Systemmentioning
confidence: 99%