2007/04/30 by Oliver Rinne, Lee Lindblom, Mark A. Scheel +1 · 3 citations
Physics and Astronomy · #Astrophysical Phenomena and Observations #Pulsars and Gravitational Waves Research #Relativity and Gravitational Theory #gr-qc
paper · pdf · doi:10.1088/0264-9381/24/16/006
published as Class.Quant.Grav.24:4053-4078,2007 · Modified to agree with version accepted for publication in Class. Quantum Grav
arxiv created 2007/07/25 · openalex publication_date 2007/07/31 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
Various methods of treating outer boundaries in numerical relativity are compared using a simple test problem: a Schwarzschild black hole with an outgoing gravitational wave perturbation. Numerical solutions computed using different boundary treatments are compared to a 'reference' numerical solution obtained by placing the outer boundary at a very large radius. For each boundary treatment, the full solutions including constraint violations and extracted gravitational waves are compared to those of the reference solution, thereby assessing the reflections caused by the artificial boundary. These tests are based on a first-order generalized harmonic formulation of the Einstein equations and are implemented using a pseudo-spectral collocation method. Constraint-preserving boundary conditions for this system are reviewed, and an improved boundary condition on the gauge degrees of freedom is presented. Alternate boundary conditions evaluated here include freezing the incoming characteristic fields, Sommerfeld boundary conditions, and the constraint-preserving boundary conditions of Kreiss and Winicour. Rather different approaches to boundary treatments, such as sponge layers and spatial compactification, are also tested. Overall the best treatment found here combines boundary conditions that preserve the constraints, freeze the Newman–Penrose scalar Ψ0, and control gauge reflections.