Cauchy-characteristic extraction in numerical relativity

Abstract

We treat the calculation of gravitational radiation using the mixed timelike-null initial value formulation of general relativity. The determination of an exterior radiative solution is based on boundary values on a timelike worldtube $Γ$ and on characteristic data on an outgoing null cone emanating from an initial cross-section of $Γ$. We present the details of a 3-dimensional computational algorithm which evolves this initial data on a numerical grid, which is compactified to include future null infinity as finite grid points. A code implementing this algorithm is calibrated in the quasispherical regime. We consider the application of this procedure to the extraction of waveforms at infinity from an interior Cauchy evolution, which provides the boundary data on $Γ$. This is a first step towards Cauchy-characteristic matching in which the data flow at the boundary $Γ$ is two-way, with the Cauchy and characteristic computations providing exact boundary values for each other. We describe strategies for implementing matching and show that for small target error it is much more computationally efficient than alternative methods.