Constraint preserving boundary conditions for the Z4c formulation of general relativity

TL;DR

This paper develops high-order boundary conditions for the Z4c formulation of general relativity that preserve constraints and absorb unwanted waves, demonstrating boundary stability and effectiveness through numerical tests.

Contribution

It introduces and analyzes new high-order boundary conditions for Z4c that ensure constraint preservation and absorption, with stability proofs and numerical validation.

Findings

Boundary conditions are boundary stable in the frozen coefficient approximation.

Numerical tests show effective constraint preservation and wave absorption.

The approach is validated in spherical symmetry simulations.

Abstract

We discuss high order absorbing constraint preserving boundary conditions for the Z4c formulation of general relativity coupled to the moving puncture family of gauges. We are primarily concerned with the constraint preservation and absorption properties of these conditions. In the frozen coefficient approximation, with an appropriate first order pseudo-differential reduction, we show that the constraint subsystem is boundary stable on a four dimensional compact manifold. We analyze the remainder of the initial boundary value problem for a spherical reduction of the Z4c formulation with a particular choice of the puncture gauge. Numerical evidence for the efficacy of the conditions is presented in spherical symmetry.