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Boundary conditions at Black Holes involve physics and numerics
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Certainly finite difference mesh needs some sort of special treatment
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Physics says that any information inside black hole is irrelevant
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It cannot get out and so cannot affect solution outside hole
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However we don't know where Black Hole is until we get full solution!
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This issue is "Show-Stopper". It may be that difficulties in this area will prevent reliable solutions without a major algorithmic breakthrough or new physics insight
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Other NR issues are hard but no reason why we shouldn't solve reasonably well
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