Boundary Conditions for the Einstein Evolution System

TL;DR

This paper develops and tests new boundary conditions for Einstein's equations that prevent constraint violations and unwanted gravitational waves from entering the computational domain, improving the stability of black-hole simulations.

Contribution

The paper introduces boundary conditions for the Einstein evolution system that effectively control constraint violations and are compatible with fixed-gauge evolutions in 3D black-hole simulations.

Findings

Boundary conditions prevent constraint violations from entering the domain.

They effectively limit the growth of constraints in 3D black-hole evolutions.

The conditions are compatible with fixed-gauge evolutions.

Abstract

New boundary conditions are constructed and tested numerically for a general first-order form of the Einstein evolution system. These conditions prevent constraint violations from entering the computational domain through timelike boundaries, allow the simulation of isolated systems by preventing physical gravitational waves from entering the computational domain, and are designed to be compatible with the fixed-gauge evolutions used here. These new boundary conditions are shown to be effective in limiting the growth of constraints in 3D non-linear numerical evolutions of dynamical black-hole spacetimes.