Boundary conditions for the Einstein evolution system

Abstract

New boundary conditions are constructed and tested numerically for a general first-order form of the Einstein evolution system. These conditions prevent constraint violations from entering the computational domain through timelike boundaries, allow the simulation of isolated systems by preventing physical gravitational waves from entering the computational domain, and are designed to be compatible with the fixed-gauge evolutions used here. These new boundary conditions are shown to be effective in limiting the growth of constraints in 3D non-linear numerical evolutions of dynamical black-hole spacetimes.

Excising das All: Evolving Maxwell waves beyond scri

“…The means for doing this have been developed, e.g. [21][22][23][24]. Then the possibility remains open that well posed wave equations could run indefinitely.…”

“…When the de Sitter option is used, one finds v in > 0, i.e., both the inward and the outward sides of the light cone point toward increasing r, for an interval around r 2. In evolution codes which permit setting the computational boundary on a coordinate sphere (such as those described in [21][22][23][24]) the outer boundary could be set at r 2 or slightly beyond in the metric described above (or ones asymptotically similar). However, if a cubic boundary enclosing # is to be used, there are additional behaviors beyond # that need attention.…”

Testing outer boundary treatments for the Einstein equations

“…As described in [27], the top four coefficients in the tensor spherical harmonic expansion of each of our evolved quantities is set to zero after each time step; this eliminates an instability associated with the inconsistent mixing of tensor spherical harmonics in our approach.…”

“…These incoming fields are proportional to the Newman-Penrose scalar 0 (evaluated for a Newman-Penrose null tetrad containing the vectors l a and k a ). Hence the physical boundary condition we use is [22,27,[29][30][31] …”

“…Because the BSSN formulations using (27) are usually second order in space, there is no analogue of our three-index constraint (3) in that system. To mimic this situation in our tests of equation (29), we also impose a CPBC on u 2 Aab as discussed in section 2.2, which together with our constraint damping terms ensures that violations of the three-index constraint (3) are exponentially damped.…”