Abstract
In numerical relativity, to study astrophysical events such as black-hole collisions, the Einstein equations for geometry of spacetime are solved as system of partial differential equations. Current simulations are usually based on socalled BSSN system of 3+1 constrained hyperbolic evolution equations for tensorial fields of various ranks.
The boundary conditions for evolved fields are given by the fact that the simulated events happen in an empty space and that far from the center the waves should propagate outwards. We analyze the usual outgoing radiation boundary conditions for the BSSN variables using potentials.
Introduction of these potentials simplifies the linearized BSSN system into a set of wave equations. We also devise modifications of boundary conditions which prevent creation of constraint violations at boundary due to the conversion of outgoing constrained waves into ingoing unconstrained ones.