2005/11/30 by Burkhard Zink, Enrique Pazos, Peter Diener +1 · 1 citation
Physics and Astronomy · #Astrophysical Phenomena and Observations #Gamma-ray bursts and supernovae #Pulsars and Gravitational Waves Research #gr-qc
paper · pdf · doi:10.1103/physrevd.73.084011
published as Phys.Rev. D73 (2006) 084011 · 14 pages, 20 figures
arxiv created 2005/11/30 · openalex publication_date 2006/04/12 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
During the last few years progress has been made on several fronts making it possible to revisit Cauchy-perturbative matching (CPM) in numerical relativity in a more robust and accurate way. This paper is the first in a series where we plan to analyze CPM in the light of these new results. One of the new developments is an understanding of how to impose constraint-preserving boundary conditions (CPBC); though most of the related research has been driven by outer boundaries, one can use them for matching interface boundaries as well. Another front is related to numerically stable evolutions using multiple patches, which in the context of CPM allows the matching to be performed on a spherical surface, thus avoiding interpolations between Cartesian and spherical grids. One way of achieving stability for such schemes of arbitrary high order is through the use of penalty techniques and discrete derivatives satisfying summation by parts (SBP). Recently, new, very efficient and high-order accurate derivatives satisfying SBP and associated dissipation operators have been constructed. Here we start by testing all these techniques applied to CPM in a setting that is simple enough to study all the ingredients in great detail: Einstein's equations in spherical symmetry, describing a black hole coupled to a massless scalar field. We show that with the techniques described above, the errors introduced by Cauchy-perturbative matching are very small, and that very long-term and accurate CPM evolutions can be achieved. Our tests include the accretion and ring-down phase of a Schwarzschild black hole with CPM, where we find that the discrete evolution introduces, with a low spatial resolution of \ensuremathΔr=M/10, an error of 0.3% after an evolution time of 1,000,000M. For a black hole of solar mass, this corresponds to approximately 5s, and is therefore at the lower end of timescales discussed e.g. in the collapsar model of gamma-ray burst engines.