Abstrakt
Among the most important systems of partial differential equations (PDEs) in numerical relativity are those of the first-order in time and mixed first and second-order in space. Namely, impressive results were obtained by several groups using so-called BSSN system belonging to this category.
While the analysis of the first-order in space systems had provided a method of construction of boundary conditions compatible with PDEs, no such recipe is available for second-order in space systems unless it is symmetric hyperbolic. We show, that introducing potentials for evolution variables of a linearized BSSN system, one can find an associated symmetric-hyperbolic system of PDEs which provides boundary conditions for the original BSSN system.