2009/08/31 by Evgeny Sorkin, Matthew W. Choptuik · 14 citations
Physics and Astronomy · #Black Holes and Theoretical Physics #Circular symmetry #Context (archaeology) #Differential geometry #General relativity #Numerical relativity #Particle physics theoretical and experimental studies #Pulsars and Gravitational Waves Research #Scalar (mathematics) #Spherical harmonics #Symmetry (geometry) #Zonal spherical harmonics #gr-qc
paper · pdf · doi:10.1007/s10714-009-0905-8
published in General Relativity and Gravitation 42(5), 1239-1286 (Springer Science+Business Media) · 47 pages, 15 figures. v2: Minor corrections, including 2 added references; journal version.
openalex publication_date 2009/10/31 · arxiv created 2010/04/30 · arxiv updated 2010/05/07 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
In this pedagogically structured article, we describe a generalized harmonic (GH) formulation of the Einstein equations in spherical symmetry which is regular at the origin. The GH approach has attracted significant attention in numerical relativity over the past few years, especially as applied to the problem of binary inspiral and merger. A key issue when using the technique is the choice of the gauge source functions, and recent work has provided several prescriptions for gauge drivers designed to evolve these functions in a controlled way. We numerically investigate the parameter spaces of some of these drivers in the context of fully non-linear collapse of a real, massless scalar field, and determine nearly optimal parameter settings for specific situations. Surprisingly, we find that many of the drivers that perform well in 3 + 1 calculations that use Cartesian coordinates, are considerably less effective in spherical symmetry, where some of them are, in fact, unstable.