Cauchy-perturbative matching and outer boundary conditions: computational studies

TL;DR

This paper introduces a new technique combining Cauchy evolution and perturbation methods to extract gravitational radiation and establish stable outer boundary conditions in 3D numerical relativity simulations.

Contribution

It presents a novel matching approach between nonlinear Einstein equations and linear perturbation equations for improved gravitational wave extraction and boundary stability.

Findings

Accurately extracts gravitational radiation in numerical relativity.

Provides stable outer boundary conditions for 3D simulations.

Demonstrates numerical convergence and stability in tests.

Abstract

We present results from a new technique which allows extraction of gravitational radiation information from a generic three-dimensional numerical relativity code and provides stable outer boundary conditions. In our approach we match the solution of a Cauchy evolution of the nonlinear Einstein field equations to a set of one-dimensional linear equations obtained through perturbation techniques over a curved background. We discuss the validity of this approach in the case of linear and mildly nonlinear gravitational waves and show how a numerical module developed for this purpose is able to provide an accurate and numerically convergent description of the gravitational wave propagation and a stable numerical evolution.