Exact boundary conditions in numerical relativity using multiple grids: scalar field tests

Abstract

Cauchy-characteristic matching (CCM), the combination of a central 3 + 1 Cauchy code with an exterior characteristic code connected across a timelike interface, is a promising technique for the generation and extraction of gravitational waves. While it provides a tool for the exact specification of boundary conditions for the Cauchy evolution, it also allows us to follow gravitational radiation all the way to infinity, where it is unambiguously defined. We present a new fourth-order accurate finite difference CCM scheme for a first-order reduction of the wave equation around a Schwarzschild black hole in axisymmetry. The matching at the interface between the Cauchy and the characteristic regions is done by transferring appropriate characteristic/null variables. Numerical experiments indicate that the algorithm is fourth-order convergent. As an application we reproduce the expected late-time tail decay for the scalar field.