Cauchy-perturbative matching and outer boundary conditions I: Methods and tests

TL;DR

This paper introduces a novel method for extracting gravitational radiation and setting outer boundary conditions in 3D numerical relativity, using Cauchy-perturbative matching to linear wave equations, with demonstrated accuracy and convergence.

Contribution

It presents a new Cauchy-perturbative matching technique for gravitational wave extraction and boundary conditions in numerical relativity, along with a numerical implementation and validation.

Findings

Achieves second-order convergence with linear wave data

Successfully matches 3D Einstein evolution to 1D wave equations

Provides a robust method for outer boundary conditions in simulations

Abstract

We present a new method of extracting gravitational radiation from three-dimensional numerical relativity codes and providing outer boundary conditions. Our approach matches the solution of a Cauchy evolution of Einstein's equations to a set of one-dimensional linear wave equations on a curved background. We illustrate the mathematical properties of our approach and discuss a numerical module we have constructed for this purpose. This module implements the perturbative matching approach in connection with a generic three-dimensional numerical relativity simulation. Tests of its accuracy and second-order convergence are presented with analytic linear wave data.