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Absorbing boundary conditions for Einstein's field equations
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A common approach for the numerical simulation of wave propagation on a spatially unbounded domain is to truncate the domain via an artificial boundary, thus forming a finite computational domain with an outer boundary. Absorbing boundary conditions must then be specified at the boundary such that the resulting initial-boundary value problem is well posed and such that the amount of spurious reflection is minimized. In this article, we review recent results on the construction of absorbing boundary conditions in General Relativity and their application to numerical relativity.
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Ill-posedness of the Cauchy problem for linearized gravity in a cavity with conformal boundary conditions
Linearized gravity in a cavity with conformal boundary conditions is ill-posed: a sequence of smooth perturbations with vanishing initial data grows without bound at every positive time.
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