Constraint-preserving Sommerfeld conditions for the harmonic Einstein equations

TL;DR

This paper introduces a new boundary condition method for Einstein equations in harmonic gauge, implemented in a 3D code, to improve the accuracy of numerical relativity simulations.

Contribution

It presents a novel formulation of constraint-preserving Sommerfeld boundary conditions for harmonic Einstein equations and demonstrates their implementation and testing in a nonlinear 3D code.

Findings

Boundary conditions improve numerical stability.

Enhanced accuracy in 3D Einstein equation simulations.

Potential for better gravitational wave modeling.

Abstract

The principle part of Einstein equations in the harmonic gauge consists of a constrained system of 10 curved space wave equations for the components of the space-time metric. A new formulation of constraint-preserving boundary conditions of the Sommerfeld type for such systems has recently been proposed. We implement these boundary conditions in a nonlinear 3D evolution code and test their accuracy.