Absorbing boundary conditions for Einstein's field equations

TL;DR

This paper reviews recent advances in constructing absorbing boundary conditions for Einstein's field equations to improve numerical simulations of wave propagation in unbounded domains in general relativity.

Contribution

It provides a comprehensive review of recent methods for absorbing boundary conditions in numerical relativity, enhancing simulation accuracy.

Findings

Improved boundary conditions reduce spurious reflections.

Enhanced well-posedness of initial-boundary value problems.

Better simulation stability and accuracy.

Abstract

A common approach for the numerical simulation of wave propagation on a spatially unbounded domain is to truncate the domain via an artificial boundary, thus forming a finite computational domain with an outer boundary. Absorbing boundary conditions must then be specified at the boundary such that the resulting initial-boundary value problem is well posed and such that the amount of spurious reflection is minimized. In this article, we review recent results on the construction of absorbing boundary conditions in General Relativity and their application to numerical relativity.